Welcome to cruise-chat. I think you made a very wise choice in planning the Exployer of the Seas. In answer to your concerns and questions...
1. Restaurants being free: Only the special restaurants have a charge. Portofino's ($20 per person) and Johnny Rockets ($3.50 per person). The main dining room, the Windjammer, and the Promenade eateries are all free.
2. Noise level: Our friends were in a Promenade cabin on our October cruise and said they had no problem with noise.
3. Long lines for rock climbing: Not long when ever I watched. Noticed I said watched...
4. Cabins to stay away from: I heard near the elevators. But, I never had a problem being near the elevators. The only noise I've encountered was people in the hall way or out on the balcony next to ours. Maybe twice in our 31 cruises.
Hope this helps. You'll get a lot more answers about your topic.