Difficult to answer this question without knowing more about the specifics of your trip. But you can't go wrong with Shinjuku if you want your hotel to be in the middle of shopping/dining and want convenient transport access to most everywhere in Tokyo.

In Shinjuku, try to pick a hotel that's within 5min walk from Shinjuku Sta. I often stay at Hyatt Regency but, to me, that place is too far of a walk from everything. Hilton's even further out from the action. Century Southern's the best for location imo, and Keio Plaza is also reasonably close to the station. Then again, Hyatt and Hilton are nicer than Keio Plaza, and you may not mind a 10min walk few times a day as much as I do. If shopping/dining/kids are more of priority than anything, you could stay in Odaiba... although the summer heat can make you sick just walking from one Odaiba complex to another (then again, I'm not even sure if you're going when it's hot). Summer hotel rates can be incredibly high in certain parts of Tokyo. Tends to be more reasonable in places like Shinagawa and Asakusa in my experience. But not as good shopping/dining in Shinagawa (although very convenient in terms of transport) and Asakusa is not the most centrally located transport-wise. If you want to spend less on everything, Kawasaki has tons of shopping/dining and still convenient to many parts of Tokyo.

I'm kind of rambling on here, but maybe this gives you a sense that there's just a lot of variables involved and that you're best off narrowing things down a bit yourself and then coming back to ask more specific questions as others have said.