Hi Debbie,
Lucky you to stay at the Hassler!
Yes, you can go up or down from the hotel by taking Via Sistina or Via Gregoriana. I agree, the steps are "fun" just once or twice!
Editing to add: I seem to recall there is an elevator or escalators in the Spagna Metro station that goes up to the same level as to where the Hassler is . I used it years ago, don't know if it's still there or not. The Metro stop is , just don't know if the escalator/ elevator is functioning anymore.