There probably is no such place as the best for the task. It is a matter of preferences accordingly to chosen technologies for the building and other, maybe even not related to technologies, factors. I mean, it depends; the place comes with the how and maybe why you do the building of ships, how much of ships you plan to build, etc.
I would go with L1 or L2 Sun-Earth, Lagrangian point and I prefer L1 over L2, because even when L2 is beyond umbra, but it is still in the penumbra (it might be a good thing actually; needs to be calculated, maybe not that big of a deal). New words I have learned today and can't wait to give you the joy to learn them today too. With Halo orbit in mind, it can really depend on future plans.
As the source of materials for the L1,2-dock, I would go with the Moon.
The reasons for the case, are the same as for any large scale construction we might wish to build in space and for the particular reason in the particular situation, there might already be a construction which helps in the ship building process.
Advantages of L1
Distance
Distance is one of the advantages of L1. Particularly its constant relative distance from the Earth and the distance is relatively close to the Earth and is about 1.5 million km or about 5 light seconds.
If we compare the solution with asteroid based locations, the problem of asteroid belt based locations - it is beyond the mars orbit and varies from 2 to 3.5 a.u. orbits and the relative distance from the Earth change from l to 4.5 a.u. over the Earth year. As a result the connection delay is 500-2'000 seconds in the best case scenario. The delay may or may not be disadvantageous, but for sure it moves the solution into more automation or more people field of implications.
Energy
At the L1-location, energy flow from the Sun is unobstructed and it is about the same as on earth orbit 1360 W/m2, but without orbital motion problems (some time in the shadow of the earth).
Compared to asteroid solutions, the density of energy is 4-12 times more than at 2-3.5 a.u. orbits and thus we spend 4-12 times less effort to get the same amount of energy compared to asteroid belt solutions. I have to note it might or might not be a problem - it depends.
Instability of L1
Instability of L1 can be considered as an advantage because any not managed debris will fly off the location (eventually), which is not the case at orbits around Moon, Earth, or at asteroid locations. (Or some debris can be dumped with use of little or zero energy in the way that it will fly to the Earth or Moon and be utilized by atmospheric braking or lithobraking.)
It might be considered as a disadvantage, as eventually, the debris can hit the Earth or the Moon, but until the debris is small enough it can be considered as an advantage. (The only problem is satellites in earth's orbit, so better to loose things in a way they hit the Moon after some period of time. Not sure if it is so easy, but needs more detailed investigation to answer the question.)
Matter/material source
One of the problems with L1, as it is an unstable location, thus there is basically nothing in terms of construction materials and such.
But having the Moon as the material source is a nice thing, because it is big enough and because same way as L1 it has a pretty constant relative distance to the Earth and is close enough to the L1 location.
Second choice for the material (including humans) source is Earth for sure.
The asteroid belt source
For asteroid location, in the asteroid belt (2-3.5 a.u. orbits) and delivering materials from there to earth orbits (not around the planet, but to 1 a.u. orbit around the Sun), if you crunch numbers for Hoffman transfer delta-v requirements (can be seen in this answer). You will get surprisingly significant numbers for moving from 2 a.u. orbit to 1 a.u. orbit 3'860 m/s first maneuver and 4'600 m/s second (you can play with the numbers here, Instacalc, Hoffman (R6 has to be 1.32692605*10^20 (G*Msun), planet radius 0), or 5300 m/s and 7352 m/s for 3.5 a.u to 1 a.u. respectively.
So, delta-v requirements for the transfer from the asteroid belt to orbits close to earth are about the same as launching stuff from earth into earth orbit. (Asteroids still preferable than doing the same from earth, but for reasons other than delta-v requirements - because of microgravity environment near asteroids, but there are higher probabilities of meteorites hitting, especially for larger constructions, as orbits near our planet are cleaned from most of debris by definition of the planet.)
The Moon as a source
As the source of construction materials and ores the Moon is preferable both to earth and to the asteroid at initial phases of the construction processes (when there is not a lot of capabilities to solve different difficulties).
The Moon is relatively good as matter sources, because everything you expect to find in asteroid belts (except water and gases, carbon) will be on the surface of the Moon, because those asteroids had bombarded the Moon since the forming of the Moon, hires moon picture here.
Some gases and carbon, water can be potentially found in some places and they are in ppm, ppb concentrations in lunar regolith. Fe, Al, Ca, Mg, Ti - are in percentage concentrations on the surface of the Moon, in form of lunar regolith (fine dust, rocks).
One of the advantages for the Moon as a material source: it is big, compared to most of the asteroids. Its big size means that you are able to build large (long) constructions on the surface in gravity fields in more or less old fashion, as we do them usually.
Escape velocity for the Moon is 2380 m/s - but potentially we can build Maglev style mass drivers to launch payloads from the Moon surface. Compared to a big enough asteroid such activity will have lesser effects on its orbital characteristics (none basically), which are important for permanent construction, which might be 1000's km long.
Another nice thing with the Moon and mass driver is its ability to deliver construction material with 0 fuel expenses into L1 location, because we can launch payloads clockwise and counterclockwise around the earth and catch those payloads sky hook style (or by other means) and keep zero average momentum of our L1 construction.
Energy wise expenses of launching materials from the Moon (about 3MJ per kg) are not that big, especially if we launch mostly raw ores and compare the energy to the energy we need to extract materials, reduce elements to their base stat. And to energies we need to produce useful products from the materials. (Energy will be a few percents in the total energy expenses for the materials.)
Bonus for L1 position
As I said before there might be other constructions, which might help in building ships. By that I meant infrastructure, energy.
The L1 location is the only point suitable to reduce the amount of sunlight which the Earth gets and thus there can be a structure which regulates the amount of light and by thus regulates the climate on the Earth. But at the same time the structure can generate a lot of energy in useful (at that place) form - electricity, heat and light. And building the construction, as useful for 7 billion people on Earth, can justify building mass drivers' on the Moon and perfecting the launching of materials and constructions from the Moon to L1.
Imaginary Elephant in the room: instability of L1
Halo orbits are pretty inexpensive to maintain and with access to the material from the Moon (with the supply of the materials) not that big of a problem to maintain (with reactive propulsion, or with possible impulses from catching materials, or might be with solar sails). Considering the excess of Oxygen from reducing metals from their oxides, which is not needed in such quantities, there is always a cheap reactive mass available for the purposes of corrections.
Another solution is to build tether like structures with counterweights to correct and dynamically stabilize the position by retracting or releasing those tethers. They have to be long, which is not a problem in those conditions, as gravity there (the difference) is less than 100μm/s2. Thus no problems to have 100 thousand's of kilometers long cables made out of ordinary materials (iron, aluminium) and it takes months do destabilize the position. The length of the cables you might need is around 10'000 km. They might have to be longer, but the required length is less than 100'000 km for sure (less than the typical halo orbit size). A slightly rotating system of those cables (,which can be used to catch the payloads,) should work well (when you orchestrate it well).
Conclusion
All that being said, go with L1 if you would like to have 100's m or km's sizes ships/constructions, habitats for the crew.
If they are smaller than that - the Moon can be a pretty ok place too.
As for radiation protection, which people are concerned about a lot most of the time: with access to prices of 2.8MJ/kg of materials, you can build the shelter as thick as it is - enough to protect the humans from the radiation.
Small constructions -> bigger constructions preferable places in that order are - orbit around the Earth, Moon, orbit around Moon, L1, Mercury.
