It might seem easy to move objects in space, but change in potential and/or kinetic energy to move a moon is enormous. It's easy to imagine that launching an entire moon into orbit would take an unfathomable amount of energy, but it takes a comparable amount of energy to move a moon out of orbit, either back to the planet or to push out out of orbit.
Quick and dirty mathematics, escape velocity = orbital velocity x the square root of 2, so if you take the orbital speed of an object (in the case of Titan around Saturn - about 20,000 Kilometers per hour), you would need to accelerate it to about 20,000 x root 2 or a bit over 28,000 KPH to get it to escape Saturn's orbit. Perhaps a hair less than that as Saturn's gravitational hold would lose out to the Suns past a certain point, but you'd still need nearly 8,000 KPH of additional velocity to get it out of it's Saturn Orbit. Then once it's escaped Saturn, you'd have an orbit around the sun - perhaps moving it towards an L1 orbit and from there, it would need to be decelerated towards Jupiter (acceleration is needed to expand orbits - away from Saturn, deceleration to contract them - towards the sun).
And, accelerating something that's 80% heavier than the moon to an additional 8,000 KPH requires a staggering amount of energy, unless you plan to spend tens of thousands of years doing it. There might be enough 3He on Titan and Saturn to provide fission fuel to undertake such a thing, but it's hard to imagine that there wouldn't be better uses for that much energy.
If you get it near Jupiter in just the right way a gravity assist is possible to send it more towards the inner solar system, but I imagine that would inevitably be an elongated orbit - not really an expert on gravity assists though, but Jupiter could help move it towards the inner solar system, then (maybe) a 2nd assist around Mars to level it out - maybe, into a possible orbit, but the timing would need to be just right. Such a project would not be easy.
You wouldn't need to get it as close to the sun as earth, cause all the CH4 would act as a powerful greenhouse gas. An orbit around Mars distance might work just fine, but it would be an enormous energy expenditure and I have a hard time seeing such a thing as practical or beneficial.
Also, as CuriousOne said - that close to the sun, with the low Gravity of Titan, it would probobly, over time, lose it's atmosphere as Mars did.
My 2 cents - leave Titan where it is and go there.