Where to sleep
We stayed with a school friend of mine, so I can't say much about accommodation. However, as Tarragona is not so touristy, the accommodation shouldn't be too expensive. The city itself is not big, so you can easily do everything on foot. Accordingly, the location of the accommodation is not so important, as you can reach everything quickly.
Alternatively, you can also stay in Salou, a seaside resort near Tarragona. In Salou, you have a nicer beach on your doorstep than in Tarragona. However, Salou is much more touristy, especially in summer.
It is also possible to take a day trip from Barcelona to Tarragona. The journey by car takes around 1 hour. The cities are also connected by rail.