TLDR: space is expensive, and not as cold as you want it to be. Without major technomagical change, it's going to be far cheaper just to store them on Earth.
Let's suppose you want to store 10 billion people-popsicles, a bit more than the current population of Earth.
A human body has volume of approximately 1 cubic metre, but since humans don't tesselate neatly, let's allow about 2 m^3 and 100 kg per person, including a frugal allowance for the structures that will contain them. So you need to store a total of 20,000,000,000 (2e10) cubic metres of peepsicles with a total weight of 2e12 kg.
Current cryo technology generally uses liquid nitrogen, which requires maintaining a temperature of around −196°C.
Currently, SpaceX are quoting \$90m for a Falcon Heavy launch, with a payload of 64 tons to low Earth orbit. That works out at about \$1500 per kilogram to LEO (more if you want to get anywhere else in the solar system), or about \$3000 trillion (\$3e15) for ten billion people. This is about forty times the GDP of the entire world. Put another way, it's about \$150k per person.
That's at current prices. Technological improvements and economies of scale might achieve some savings, but a large chunk of the cost is kerosene-based fuel, which is a limited resource and likely to become more expensive with increasing use.
Unfortunately, even when you get to LEO, space isn't actually that cold... on average. While most of the "sky" is at a nice frosty three Kelvin, there's a great big fusion reactor in one corner of the sky radiating heat at six thousand degrees. If it can keep Earth warm, it can keep a nearby satellite warm too - it won't be quite as warm, because of the lack of a greenhouse-effect-inducing atmosphere and tidal/radiothermal heating, but the black-body temperature for an object in LEO is a few degrees above freezing.
This means that if you want to keep your peepsicles at liquid-nitrogen temperatures in anywhere near LEO, you're going to need a lot of refrigeration... which is really hard to achieve in space. You can't conduct or convect heat away, so your only option is to radiate it. Black-body radiation varies with the fourth power of temperature, so an object at −196°C (77 Kelvin) will radiate about 1/160th as much as the same object at room temperature.
You can improve things a bit by keeping a reflective shield between your space station and the Sun, but even a small amount of heating through the shield is going to be very difficult to counteract. To stay at cryo temperatures purely by passive means, you're going to need to go a long way out, and as you've noted, that steeply increases costs.
Next consideration: how are you getting those people back from wherever you choose to keep them? If you want to retrieve them from anywhere other than LEO, then you need to expend a lot more energy (rocket fuel/etc.) to recover them... and unless you have a convenient fuel supply located near your storage facility, you need to spend even more energy to get the fuel out there.
Retrieval from LEO is a bit easier, because you can take advantage of the Earth's atmosphere for braking. However, that tends to be a rough ride, and cryo-frozen humans are fragile things (a friend of mine who used to work in the industry used the term "meatglass"), so you're going to want some good shock absorbers... which ups the weight.
Unless your setting includes some developments that drastically reduce launch costs, it's hard to see how this would be cheaper than storing people on Earth. If you're willing to stack people ten high, you can fit them all in a footprint approximately 30 x 30 km; that's probably less than you'd need for the launch pads and kerosene refineries required to launch them into space.
Sorry to be a downer here!