We did the Best of Spain trip in 2014 and flew into Barcelona 4 days early. It was wonderful to have the extra time as there is so much to see and do in the city. Our tour hotel was NH Barcelona Centro. We booked the extra 4 nights there. It was a great location, central to everything and close to public transportation. I would recommend staying there, especially if that is the tour hotel. Remember that if you are staying in an alternate hotel, you will have to pack up all of your things, need to make sure that laundry is dry, and transport to the new hotel, and maybe not be able to check in right away. That can take up valuable touring time on the first day of your RS tour. You can save a little money if you book the room without the breakfast buffet. We don't eat large breakfasts, so just bought yogurt and fruit at a nearby store on our mornings before the tour started. The breakfasts there are pricey, but very good--lot's to choose from.
I would also recommend at the end of your tour to go to Cordoba to see the Mezquita, either as a day trip from Sevilla, or as a stopover if you are taking the train to Madrid for your flight home. Well worth the extra day.