The above original post was for the Hyatt Place San Jose Airport but I am going to assert moderator privilege and retitle it to include the close-by Hyatt House, for which I didn't see an existing thread. Granted they aren't /directly/ next to each other as some other HP/HH combos, but they are pretty close, and they share an airport shuttle, and since this makes two posts in 6 years, it seems reasonable
Anyway I stayed here after a lateish arrival into SJC. The property info says hotel shuttle until 11pm, but on texting the hotel, the shuttle is on request, and last call is actually at 10:30pm, not 11. There is a free alternative in the form of the VTA 60 bus, which is free if you board at the airport, and has luggage racks -- make sure you get on one headed to Milpitas BART -- closest dropoff is at Brokaw & 1st St., catty-corner from the HH. However it only runs once every 30 minutes at that hour.
Greeted as Globalist, offered daily waters from the mini-market next to the front desk (including at checkout) and proactively offered late checkout. The elevators are slow and only one seemed to be in service; my room was on the 2nd floor but each time I was about to give up and bail for the stairs (which are at either end of the property away from the elevator) it started to come back down again. Other than that, it's a Hyatt House, not much else to report (I didn't have breakfast there).