Wedding Rehearsal Dinner in Manhattan for 100 People
For that many people you probably are going to need to rent out an entire restaurant as most places are not big enough to accommodate that many people in a private room. So in that way, you really can pick your style of place. Not sure if this is your thing, but I did see someone rent out the entire bottom floor of Hill Country for a rehearsal dinner and it looked like a pretty awesome time. Most likely would be right in your price range.
We looked into Hill Country for our rehearsal dinner. We had 40 people, so we wouldn't have been able to rent out the whole bottom floor and they had a rule that there couldn't be any speeches if you didn't rent the whole floor, but I think with 100 people you'd be able to get the whole space. From what I remember (our wedding was 3 years ago) it would definitely be in your price range. They were very nice when we went to see the space, so I'd definitely recommend checking it out.