The ancient romans were ahead with regard to body care. I Patrizi (the rich people) had relax at Termae (ancient spa), i poracci, the poor people, did the sauna, on the street, carrying stones! Two thousand years after nothing has changed, the spa is still a symbol of riccanza (opulence). If you are looking for relaxation and wellbeing in the places of the ancient romans, I would recommend two places. Try Aquamadre, just behind the imperial ruins, has very suggestive rooms, some Jacuzzi and a long range of facial and body treatments.
Something more oriental is Kamispa, just a short walk from the Trevi Fountain. Also here is the relaxation area and massage rooms.