There are several possibilities.
TRAX (Light Rail)
TRAX trains depart the airport every 15 minutes on weekdays and every 20 minutes on weekends. The Green Line (which is the one that goes to the airport) will take you to within two blocks of the hotel with no change in trains. You board TRAX at the far end of Terminal One and take it to Gallivan Plaza (at 200 South Main Street). It is about a 20 minute ride. Once you exit TRAX, walk west (right) on 200 South one block to West Temple, turn right and walk a half block to the Hilton. The one-way cost is $2.50. The senior fare (over 65) is just $1.25. (Down side - if you arrive at terminal 2, it is a long walk to the far end of terminal one. And, city blocks are bigger than those you may be used to . So, if walking is a problem, take a shuttle or taxi.)
The Hilton contracts with Haroon Transportation for shuttle service door-to-door from the airport to the hotel. Call Haroon at 855-316-6888 once you retrieve your bags at the airport and they will come and get you. The one way fare is $12 per passenger
A taxi will cost $20 to $25 for any number of passengers and so is a good alternative to the shuttle for 2 or more people