You only have 12 days. If you choose Guatemala you give up on beaches but there is lots to see and lots of hiking possibilities. As you seem to want to climb volcanoes look at Acatenango overnight (Antigua).
Forget the scooter. Buses are cheap. Shuttles are available as well.
Make a list of budget hotels. Go down the list when you are there. You will also stumble on hotels that were not on your list. And often cheap hotels don't have an online presence.
I would start with Lake Atitlan for 3 days. Take a boat to Santiago (and don't miss Maximon). Take a boat to San Pedro and also visit San Juan. Take a boat to Santa Cruz and hike from Santa Cruz to Jaibalito and (with a guide) on to San Marcos. From Panajachel take a pick-up truck to Santa Catarina Palopo (or walk). Go to the nature reserve in Pana (hanging bridges, waterfalls, ziplining). Go to the Solola market on Tuesday or Friday (a short bus ride from Pana).
Then two days Antigua or three days if you are climbing Acatenango.
A shuttle to Lanquin and a day (or two) for Semuc Champey (scenic stepped pools, swimming, tubing, caves...).
A shuttle to Flores and stay overnight at Tikal (the hammocks are great). If you have time visit Yaxha as well.
Overnight bus back to GC (or fly).
Rio Dulce is nice for the scenic boat ride to Livingston and a few nights in a jungle hostel like El Hotelito Perdido. Lots of people like it there but it was not my favorite area.
Copan is nice for a day or two: ruins, scarlet macaws (but you can see lots of them at the ruins), hot springs.
Nicaragua would be great for 12 days as well. Granada for a day and active volcano Masaya (you will see lava) and Laguna de Apoyo for swimming and kayaking. Ometepe Island for the two volcanoes (both tough climbs), waterfall, nature reserve with nice beach and wildlife, natural spring pool, kayaking... Leon is a great colonial city with amazing volcanoes (Cerro Negro has great views, active crater and you can board or run down and Telica has a very impressive crater and you can stand right on the edge) and great beaches like Las Penitas and Jiquilillo.