There is a couple of local buses from the transportation terminal that go to Mo Chit for maybe 50 baht max. There may also be a van service for about 120 baht. You have to take the shuttle to the transportation terminal.
Route 9905: Mo Chit - Suvarnabhumi airport - Laem Chabang - Pattaya
Route 9906: Mo Chit - Suvarnabhumi airport - Rayong province
They stop at the local bus station which is next door to the Mo Chit II (northern terminal) and you'll have to hump you bags maybe a 1/10 of a mile. I find its easier to take a cab from the Airport for 300 baht.
Buses to Chaing Mai are on the first floor. They have day buses but they stop every place. The afternoon (after 4 pm) buses are more direct. Get a 24 or 28 seat bus as the 32 and 40 seat buses are uncomfortable on a 10 hour ride (expect to pay about 600-800 baht). We take the 999 bus (Gow, Gow,Gow) but they also have VIP. They'll give you some water and a light snack. Near the restrooms you can park your bag all day for I think 30 baht and the toilet is three baht. Mo Chit also has a 7/11 a Dunkin donuts and a KFC plus many local food vendors. During the day you might go over to Chatuchak for a couple of hours but there's really nothing else near. Not too many farang in the Mo Chit station and they don't have any English reading material so bring your own. They have Thai TV but it repeats after about 2 hours.