If it were me, I'd probably get either the Playstation 3 (PS3) or Nintendo Wii. The Playstation 3 should be able to play a good number of older Playstation 1 and 2 titles giving it a very broad selection of games across a wide set of genres. Problem is, it's very expensive.
The Nintendo Wii is likely to have a number of games that might be fun for the whole family to play. The novelty of some of it might wear off over time, but it might work well for short visits of a week or less. It's not nearly as expensive as the Playstation 3, but it's much harder to come by. Most stores are having difficulty keeping them in stock.
The Xbox 360 does have some ability to play older Xbox games, but it's fairly limited, so you're largely confined to Xbox 360 titles which are going to be mostly first person shooters and your general action adventure sort of game. Probably not the best choice if the intended audience is visitors. It's also a bit on the expensive side like the Playstation 3, so just another nail in the coffin.
The Playstation 2 might not be a bad choice either. It's an old system, so it's cheap, has an extensive game library, and also has full compatibility with older Playstation 1 games. It won't be able to play many, if indeed any, of the latest and greatest games the grand kids may want to play is the major down side to it.
That is my opinion anyway. Hopefully this helps you in making your choice.
I have 3 grown kids with 7 grand kids. All have video games but they are different with each household. I want to get 1 for here when they visit but can't ask the kids as each thinks something different is better. DO you know that feeling? Anyway I need t know recommendations for kids from 16 to 7 so I can get one for all to play. I see PS2, ps3
Xbox and 360 as well as natindo and Wii. Can someone give me some advise?