There are a bunch of such towns/cities throughout the US.
Kansas City is likely the largest and the most famous one, on the boundary of Kansas and Missouri.
It also appears that there are a lot of not-so-black-and-white choices too, as some towns have boundaries in the MIDDLE of them, other towns stop, and start up on the other border, etc. It's all a bit of a mess, and so to give a precise number as an answer for this question is impossible.
However, a complete list of towns (61 candidates) with borders near/straddling/sharing more than one state is here:
Sioux City, Iowa, is 'in' Iowa, South Dakota and Nebraska (North Sioux City is in SD, South Sioux City is in NE, but they are continuous, not separate places, for all practical purposes). I was there 2 weeks ago and it was very confusing. Omaha, NE, also has a section (Cedar Lake, near the airport) which is a little enclave of Iowa, so we drove into it for gas, which was cheaper than in Nebraska!
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