Ok, I'll "nerd" out a little bit because I love Yamaha grands.
I bet, based on the bench, that the piano is about 30-35 years old. And I bet it's a G-series. I'm not good with estimating sizes, especially from this angle, but either 5'3" or 5'8" (I'm guessing probably 5'3").
Who thinks I'm wrong?
In all seriousness, Operator, this is potentially really great. Yamaha makes very nice, durable and reliable instruments. And even if it's long neglected, it may tune up very nicely. And, as you say, you might spend $2000, but that could get you a very nice Yamaha grand. It's not likely you could get a nice instrument for that amount of money otherwise.
You also don't have to ask them to remove everything from the top of the piano, you could probably get a lot of information (age and series/model) just by removing the objects at the front, flipping up the lid at the hinge (rather than opening the lid completely) and then moving the music desk forward or back. That should let you see the serial number (which will be in black) and the series number, which will be raised up in the plate itself.
I just googled and found these photos, this is the info you're looking for:
If you have it inspected/evaluated by a piano tech, though, they will need to take everything off the top.
But first get the serial number and model number and that will allow people here to give you a ton of info.