We went a while back now, when some friends were in town - and I think that it's one of those things that is a must do if you want something truly different when you visit. I don't know anywhere else at all where you can get this kind of experience.
Some tips I would give if you're visiting the Robot Restaurant are:
Book in advance
This place fills up, even with four sessions a day. The night that we went, I didn't see a spare seat at all - and it's a relatively small seating venue. If it's on your must do list, you can pop on over to their website here to book online. It's in English, so no worries if you can't read Japanese - it's step by step and user friendly! You can either pay online with your credit card, or choose the payment on arrival method to just pay when you get there.
Eat Before (or after) you go
At the time we went, they were serving a bento box for dinner which was included as part of the admission fee. In saying that, it wasn't really something that we enjoyed or that was substantial! From their website currently, it seems like they offer a paid bento box option on top of the admission cost (it's 1000 yen extra for the bento), but I would recommend just eating somewhere else beforehand or waiting until the show is done. You're in Tokyo - there are eateries galore just outside that will be better as well as probably cheaper, too!
Be prepared for a million lights and a lot of noise
I feel like this probably goes without saying, but be prepared for a noisy evening. Our ears were ringing once we got out! Expect it to be on par with a loud concert or thereabouts - we had some friends in our group that had to head out and catch their breath for a bit at the intermission break because I don't think they were expecting it to be just as loud as it was!
Understand that even the bathrooms are probably going to be the wackiest you've seen
Nope, your senses won't get a break even when you need to go to the bathroom. Gold fixtures, mirrored tiles, and a floral printed toilet? I'd almost venture to say that seems kind of normal for this place - especially once you see the show!
Soak it up and realize it's probably a once in a lifetime thing
Now that I've been to the Robot Restaurant, I don't feel any need to necessarily go back and do it again (although I do recommend it to people when they are in town visiting!) so just enjoy how full-on and bizarre it is! It's one of the weirdest things we've done here, but also incredibly memorable. The most feedback I get from people when they do go as part of their vacations tends to be along the lines of "that was crazy...but awesome!" and I think that accurately sums it up.