Tropic Air flies from BC International to Flores, Guatemala where you can change to a TAG flight to Guatemala City. From there, your on your own.
Express buses depart BC daily to Flores. Change to another express bus to GC.
The bus details are on the BelizeBus site...
Taca is another airline that flies from Belize City International. Go to their website to see their destinations.Edited: 06 June 2013, 15:06
I would split Belize and Antigua into two separate trips; they're just too far apart - unless your goal is a leisurely tour of the region.
Merida is a good Antigua substitute. Closer, but again, deserving of a separate trip. Belize has no comparable places.
For something different, ditch Antigua and check out Livingstone, Guatemala.Edited: 06 June 2013, 17:50
Livingston. Nah, forget it; there are similar places closer to you.
Are you planning to see anything in western Belize or to visit Tikal? Based on answers, my recommendations might change. Happy trails!