I prefer a private home over a restaurant, both as a guest and a hostess. As a hostess, you do have to prepare and cleanup in a home, but you have more control over cost. If you go to a restaurant, most people will not order some crazy expensive item, and two glasses of wine, but their is a chance someone will. As a guest, private homes seem more relaxed, people can be as loud as they want to and not have to worry about disturbing other patrons.
As far as games:
I like the game where everyone starts with a clothespin clipped onto them (there shirt or purse or something). The game goes that you cannot cross any part of your body - hands, feet, legs, fingers... - if someone catches you then they get to take your clothes pin and the person with most pins by the end of the shower wins. Alternately I've seen it played where you can't say a certain common baby-related word. Like "baby" and if you do, the person that catches you gets your pin.
Another game I like is the one where there are a list of items that are commonly found in women's purses (some baby related or not) and the woman with the most items wins. The list would include things like:
kleenex, nail file, safety pin, hand sanitizer, lotion etc.
Fianlly, what ever you do, please don't play the "game" where everyone addresses their own TY note envelope and then have a raffle where you pick one of the envelopes and give the "winner" and prize.