Hola tio,
While you certainly could stay in places like Tarragona or Sabadell, I think it might seriously impair your ability to go out and enjoy Barcelona, especially at night. For example, I'm not sure about the RENFE trains to Tarragona, but the last weekday FGC train to Sabadell leaves Barcelona at 11:50pm, which is pretty early by Barcelona standards. Also, after a few trips back and forth, you might start to wish you were a lot closer (I commute each day from Barcelona to Terrassa, which is right next to Sabadell, and the 90-minute round trip gets old very fast.)
A better option might be to find a hotel away from the Barri Gotic/Ciutat Vella area but still close via the metro. There's one in our neighborhood called the Husa Bonanova Park; it's on a fairly quiet street in a residential area, but only about 5 minutes' walk from the Maria Cristina metro station (which gets you to Plaza Catalunya in about 15 minutes). According to the website (
www.husa.es ) they have rooms for around 55€, with on-site parking. I've never stayed there personally, although my mom did last year and said that it was fine for her.
I'm sure others might have some similar suggestions; my advice, though, would be to stay as close as your budget will allow, so that you can spend more time enjoying the city and less time traveling back and forth.
Hope you have a great trip!
-greg