The name of the hotel that is at the airport
The hotel inside the airport is the Hyatt Regency Orlando International Airport. I did a one night stay with 2 adults and 2 kids and the lowest rate was $135, and went up from there.
However, there are MANY hotels that are very close to the airport, and the majority of them offer a shuttle service to and from the airport. For example, all within 2.5 miles from the airport there is Courtyard By Marriott, Hampton Inn Airport, Holiday Inn Select, Fairfield Inn, La Quinta Inn North, Renaissance Orlando Hotel Airport, Amerisuites/Hyatt Place Northwest Hotel, Crowne Plaza Orlando Airport, Hilton Garden Inn, Residence Inn, and Wingate Orlando Airport. There are actually more, but that would this post really long, lol.
Also, I can tell you that this area is nice and safe. My DH works in this area (we live in Orlando, lol) and we drive through here all the time. Hence the reason I know they have shuttle buses. If you looked up some of the hotels, I'm sure their websites will tell you if the shuttles are free or not (but I'm assuming the majority of them are, as that would be a plus to get people to stay there).
Hope this helps!