I've done both domestic and international flights arriving there and it isn't like Don Muang .... no really separate terminals that I noticed, not that I'm very observant. However the new airport is quite big ...lots of pointlessly long corridors wherever you go/come from. I'm sure I saw a "meetings" area in the arrivals area somewhere. A quick google gives this spot.
Terminal Map - Level 3 - Meeting | Suvarnabhumi Airport | New Bangkok Airport Guide
Otherwise just look at the same website and decide on a suitable bar/coffee shop. Or you could arrange to meet near the taxi departure area which was downstairs last time I looked. Saw rumours somewhere it was going to be moved to upstairs but hopefully they will put signs up, if not just ask.