There is no public transportation between IAH and Kemah
(a driving distance of 50+ miles)...
Also, while there are a number of hotels that likely look close to Watergate, clustered for the most part on NASA Road 1 or west by the Gulf Freeway, there are no good transportation options to get you to Watergate from them either. The closest "brand name" hotel
to the marina is the Holiday Inn Express at the corner of 146 and 2094 (The Boardwalk area). From there it is about a mile and some change -and not particularly pedestrian friendly- walk west up 2094 to Watergate.
and its environs represent the quintessential car town. You are very much isolated without your own transportation. So I'd recommend renting
One thing you might consider is to take one of the shuttles down to Clear Lake (most locals refer to the whole area including Kemah
and League City as "Clear Lake") then rent a car down there, so you don't have to trek back to the airport
to return it. Lots of folks do that and all the rental agencies have branches nearby.
I lived for a number of years there, so feel free to pm me if you have any questions...