Depends what side of town you are on and whether you plan to compete amy/pro or are just looking for good training. For competitive level training AMC is good for the East Side. Ivan Salaverry's place is down town and Ringdemon offers MMA with KB and Boxing in Tukwila.
Why Ringdemon? Demon Mixed Martial Arts
All the local JKD/FMA places seem to offer MT these days. Northwest Kali JKD in Federal Way and MKG Seattle both have good reps as recreational MT places. They are not turning out fighters.
Cappy's and Bumble Bee are probably the best boxing gyms although there are some more recreational type boxing gyms as well.
George Credit has been turning out some decent female boxers and trains out of Judo Champions gym in Renton. The also, of course, offer Judo. They have kinda of a funky attitude down there but quality instruction.