Not at all sure I would move a water heater 3 feet unless it is blocking car access of something, but that is your business.
As for the alcove - be aware that if it has a door, you need top and bottom air vents or grilles of certain size (see owners manual or check at manufacturer website for required size) to provide air to the water heater. Quite small vent area if electric, but substantial area required if gas or oil fired, so while it will keep its little alcove warmer if it has a door, with the ventilation it might not make as much difference as you thought it might. Also - some code areas require combustion devices be at least 3 feet from any door, so if that potentially affects you check with plumber or local building department.
As for being flush with garage floor - if the alcove is in the garage (as opposed to being a totally outdoors utility closet (if in area without freezing weather) accessible from outdoors, then it has to be up on a pedestal or platform - typically 18" off garage floor but different in some areas, and also has to have fireproof surface or be built of non-combustible materials in some areas. In some code areas they apply the elevated platform requirement to only oil and gas-fired heaters (and boilers/furnaces), in many others all water heaters have to be elevated regardless of how powered. The requirement is to reduce the risk of explosion from any gas fumes from the cars, which both vent gas from tanks and sometimes spill gas on the floor if they were filled to the top of the tank when cold, then heat up in the garage.
Cost - I would expect, assuming decent access, building an alcove with ventilated door probably about $400-600 (unless your other alcove is already built), moving the heater and extending plumbing (gas and water) to it probably about $300-500 for plumber. If electric heater, probably another $150-300 for electrician depending on your local labor costs and on whether moving closer to or further away from the breaker box, plus maybea couple hundred for a handyman to repair drywall after wire move and repaint - unless you are going to DIY on that. Reason for the difference is in some code areas they do not allow splicing high-amperage feeds like that, so if moving further from the breaker box that could require running a new, longer lead all the way from the breaker box (which I presume is within 10 feet or so). In other areas, he can just put a junction box on the wall at the existing wire location, and splice in a new feed in BX conduit from there to the heater.
So - all in all, I expect your $2500, unless you live in NYC or Boston or other city like Frisco with unbelievable code requirements and very high labor and permit costs, is probably high by about half to two-thirds, especially if gas/oil fired.