You should look into Xunantunich near San Ignacio. I think that's the closest ruin to an airport you can fly to from San Pedro.
If you fly/boat into Belize City you are looking at a decent length trip to get to any ruin.
Another option would be fly direct to Orange walk and get taxi to Lamanai.
If you are feeling more adventurous fly into Flores Guatemala, and visit Tikal.
All of those options require only a short flight and short taxi/bus ride.