Hotels around Spanish steps are expensive. The 4-star Hotel Homs is 200 meters from the Spanish Steps, on average 150 € / night for a double room, or the 5-star The Inn at the Spanish Steps, a small luxury hotel offers double rooms in offer at around 150 € / night.
Tram n.2 connects Piazza del Popolo/Spanish steps with the Flaminio area in minutes. You have many affordable hotels in Flaminio area. For example, the River Palace Hotel in Via Flaminia 33, Hotel Villa Glori in Via Bernardo Celentano 11 or Best Western Hotel Astrid Roma in Largo Antonio Sarti 4.
If you are looking at booking vacation apartment, indicate Piazza di Spagna as your neighbourhood on airbnb or booking.com. You can then view the apartments on offer and the distance from Spanish steps. In any case, do not be fixated on one particular area - there are many good areas for you to consider.