Really would be hard to beat this place. Gorgeous apartment with everything you would need for a week or a month. Within walking distance to everything within the old city (Ciutat Vella). For everything else- bike it. Numerous bike rental places. Our favorite (and ubiquitous) option was Valenbisi- €13 gets you a 7 day card to rent bikes from automated rental kiosks literally everywhere. A 30 min or less ride is free and after that you’re charged by the hour but it’s practically peanuts. 30 min gets you virtually everywhere, including the beach and there are dedicated bike lanes nearly everywhere.
The Mercado Central is a five min (or less) walk. Don’t miss it. Most businesses in the city conveniently accept major credit cards but you’ll need cash there. Thankfully 3-4 banks are across the street.