Living 'here' and not being in the tourism industry makes my potential recommendation on lodging very irrelevant, however, since you mentioned your passion for everything Roman I'd like to share some sites that might interest you and that you might or might not considered already:
- The Festival of Tarraco Viva (Catalan for 'Tarraco Alive') held in May. It's a real gem. Tarragona (former Tarraco), as you possibly know was the capital of the biggest most western province of the Roman empire for several centuries and accordingly its ruins and remains, many of which have been very well preserved, present an excellent opportunity for better understanding the Roman culture, possibly right after the city of Rome itself. More info here, and video here.
- The remains of Roman Barcelona at the MUHBA located underneath the Medieval heart of the city at the Museum of History of Barcelona, in Plaça del Rei square.
- The ruins of Empúries in Costa Brava, north of Barcelona -not Roman but a tad older, from the Greek colonisation of Catalonia, but possibly equally interesting to you as per their size, conservation and importance in Western Mediterranean development.
- Next June, at the area around Creu Coberta street in the neighbourhood of Sants, west of the city, the Fira Romana (Roman Fair) will be celebrated for the sixth time. The official name is "VI Barcino·Colonia·Romae" and it's organised by the Association of Small Businesses of the area in cooperation with the City Hall and the Museum of Archeology. It's a sort of an open air market in which visitors can taste Roman dishes, see performances, attend conferences and impregnate in the life of a typical day in Barcelona during Roman times. But be aware that it's a rather humble fair and the main purpose is to educate the general public -especially children- so if you're nerdy on the issue it might not suit you much.
For a complete list of Roman sites in Catalonia check this wikipedia page. It's in Catalan -the local language- but Google Translate will work wonders ;))
You might also want to contact this TripAdvisor member, Oriolense, who is a local of Tarragona and very passionate about his city, since I'm sure you might profit from his advice.
If anything, regarding lodging, you might like to check a place near the maze of small streets and back-alleys in the Old City located between the Cathedral and the Roman amphitheatre and which happens also to be the 'highest' point of the city. Check this map.
Enjoy!