The Hyatt Place is almost as close to T2 as the Marriott/Sheraton/Hilton/Hilton Garden Inn are to T1.
There are two rental-car drop offs, one in T1 and one in T2. You can use either one. From the T1 drop-off, you can walk to the Sheraton and the Hilton (the Sheraton being slightly closer). From the T2 rental-car drop-off, you can walk to the terminal building but you'd need a quick shuttle ride to get to the hotels in the Gateway Gardens area (Hyatt Place, Holiday Inn, etc.).
Lastly, you can walk from the train station to the Hilton/HGI (they are in the same building as the train station) and the Sheraton (which is in an adjacent building that's directly connected). It takes a bit longer to get to the hotels in Gateway Gardens from the train station. You'd take the hotel courtesy shuttle from T1. (The courtesy shuttles pick up at both T1 and T2.)