I use booking.com for hotels, there are a couple of chain hotels, including a Hampton Inn in the mall area near the station, if you want something a bit more quaint, there are several places in the nearby city center.
For getting to the airport, the train is best, lots of direct trains, takes about 30 minutes, simply tap in and out with your credit card. Same with getting around.
Utrecht is nice, lots of restaurants and shops along the canals. There are several museums, a Rail museum if that interests.
Amsterdam is a short train ride away, Leiden about the same, and really most places in the Netherlands are not that far. Utrecht is a pretty central transport hub.