My mother-in-law is selling her house in Charlottesville and has offered to give me a gun safe for free.  I have to get it out of the house and relocated across town to my location.  

It's going to be a bitch to move and I'm willing to pay a service for this relocation.  Does anyone have recommendations?  Rough ballpark of what this will cost me?

Fwiw I recently got estimates in Nova ranging from $800, $1200 and $2000 to move two large heavy safes. One was 1500lbs, the other 1800lbs. The $800 guy never got back to me. The $2000 guy said he forgot to give a discount after I never called him back and came down to $1500. I chose to do it myself and it cost me just under $400.
Assuming you don't have stairs to deal with, if you want to tackle it, it aint hard, you just need to rent the right equipment to do it safely.
1) roto dolly, it's actually two dollys that strap to opposite sides and allow you to jack the safe off the floor/pallet and roll it outside and drop it onto a pallet (don't even think of not bolting it to the pallet). This dolly also allows you to move the safe sideways through a doorway. About $40/day
2) electric pallet jack gets the safe+pallet onto/off-of the trailer. About $175/day. This machine is worth it. Sunbelt has them.
3) Air-Tow trailer. This is a special trailer that has no axle under it. It drops down to ground level--FLAT (important). Air-Tow is the only brand that does this AFAIK. About $150/day. Sunbelt does not have them.  
4) Heavy duty tie down straps. Don't even think of going anywhere without tie downs front to back and side to side.
5) Rental truck if you don't have one.

If on the other hand you have stairs or a yard to go across or just don't want to deal with it, call Steve at sevenothreefiveseventhreefourthreeninefour. He has all of the above plus a stair climber. He is in Nova. Have no idea what he would charge.

I’ll second and third Steve.

Bought my first safe from him and he moved it into my first floor apartment.

Bought my second when we bought our house and he picked up the first safe and got both into a basement with very narrow exterior basement stairs and some tight turns via his stair climber/zero turn mover.

Not enough room to get enough dudes on these things to manhandle them.

Been over five years, but I believe Steve charged $300 for a move without the machine and $600 if he had to use it. The price increase is due to the machine being a custom built thing with treads that cost $1,800 per pair, if I remember correctly.

Woodbrook Sports owns the Liberty Safe Store in ashland, Va and I think they also have a store in Charlottesville. Call them, they will move the safe for you, they have the electric driven stair climber.  Best $350 I spent during my last move.

Kenny Hale at Liberty Safe of Richmond. He has been moving safes in the area for over 20 years and knows what he is doing.
He lives outside Charlottesville so it will be local for him.

I also recommend Steve's Services.  He is good to work with and reasonably priced.

Steve is the man. I have known him for a quarter century.

Because what he does is in such demand, he can be hard to get ahold of.

Thanks everyone.  Great info.

Good to know, since Steve sometimes gets overloaded or goes MIA for a bit from time to time.

He's also not getting any younger and while the stair climber is certainly a life saver, it's not a low impact job when you consider all the 3/4" plywood and whatnot he moves around making ramps and the like to solve each move's unique issues.

OP, out of curiosity, how heavy is the safe you are trying to move?

Hire it out.

One way to move them is on 4 inch Schedule 80 drain lines.

Use the pipe as rollers.

On earth, use 3/4 inch plywood for the rollers to move on.

Over the years I have done about a dozen this way.

We even slid some down interior and exterior basement stairs on a bunch of 2x lumber.

I used the Liberty safe guys from Ashland to deliver my new safe.  No issues