Interested in exploring Central America! Ideas please!

For 3 weeks, I would not run around central America. Panama takes 3 weeks to visit.
Best regards from Panama.

Maybe a week in Belize and 2 in Guatemala, maybe a couple of days in El Tunco, El Salvador for some surfing.
Start off on Caye Caulker, great diving/snorkeling and an excellent place to meet other travelers. San Ignacio, ATM cave trip and other good hiking options.
Cruise over to Tikal, over to Rio Dulce, maybe Copan and on to Antigua and Lake Atitlan.
Nebaj is noted for excellent hiking. About a 5 hour shuttle get's you to El Tunco.
Obviously you can't do all this but you could do a lot of it.
November would be a better month.
Fly to Belize City and out of Guatemala.

great advice from Joe, and Im not surprised he is helping us with plans around the US and has been super helpful.
Surfing tends to be on the pacific side and diving on the carribean side.
Surfing and partying - El Tunco in El Salvador; San Juan del Sur in Nicaragua and numerous places in Mexico come to mind. Hiking - all over Costa Rica; great volcano hikes throughout Nicaragua, El Salvador and Guatemala.
Diving and partying: Caye Caulker Belize (and then do the 3d/2n Ragamuffin trip down the coast of Belize - great fun); Bay Island Belize - Utila probably your best bet.
I think your best bet would be Belize in just 3 weeks would be similar to what Joe has said:
Caye Caulker Belize for snorkeling/diving fun - Ragamuffin sailing trip down to Placencia; bus down the coast and take a boat into Livingston, Guatemala (plenty of party there); down the Rio Dulce (maybe a night in a jungle lodge for kayaking etc) shuttle from Rio Dulce to Semuc Champey (near Coban)- high adrenalin caving and tubing with millions of backpackers in tow; shuttle to Antigua for party and a couple of days of colonial town; shuttle down to El Tunco, El Salvador for surfing.
The shuttles are fast, full of 20 something travelers, and reasonably cheap.
This is a very popular route.
If you found spare days - Lake Atitlan for hiking (and partying in San Pedro); Quetzaltenango for hiking; Tikal for ruins
Other alternative is Mexico - all your activities can be done there.

The best diving is Belize and Bay Islands Honduras, caribe side. The nest surfing is on the Pacific side, with Costa Rica the mecca for surfers from novice to pro. El Salvador has some surf, as does Nicaragua & Panama.

Sept is rainy season, and each coast and country have different weather patterns, same for Nov, still rainy season but tapers off drastically as Dec approaches which is start of Dry Season.

With just 3 weeks, you have time for 1 country and a side trip to another country.

Based on your Interest, I would go to Guatemala/Honduras, or Panama. Border crossings take a lot time and not as easy as you think overall.

If you didn't have the diving in the mix, then Nicaragua/Costa Rica...

Thank you everyone for contributing with well thought out ideas and providing me with a great direction to start planning my trip. I'm really liking the sounds of Belize and El Salvador!