Thanks for all the thoughts and suggestions. Since everyone is focused on places to stay, I think that my other implicit question (how much hassle and time involved in immigration and customs) is answered.
Oddly, all the city Hilton show up in search as being 1-3 miles from the AIRPORT. But 40+ minutes by taxi. I understand (now) this is wrong. (Why? doesn't matter.) So I have found some decent near-airport options for less than the cost of a drink at my current airport hotel (SFO).
Again, thanks.