I see two ways of answering this: if I were playing and if I were running.
Playing: If I were able to play every day for a week I would probably treat it like most conventions I go to and try out as many different games as possible. I’d try to cross off as many games off my bucket list or check out the newest, hottest games.
Running: If I were running games for a whole week I would probably set up shop at a nice big table and run the very same West Marches style D&D game all day for every day. This whole situation assumes a lot, so let’s just assume that this won’t drive me crazy or eventually bore me. I would love to run a constant game that evolves as players come and go throughout the week.