My son in Seattle found another mystery tree for me! It's large with rough grayish bark, with lancate(?) leaves around small red fruits that I swear look like cherry tomatoes!
It could be winterberry (Ilex verticillata) which is a holly. The berries are an important winter food source for birds. It is actually a shrub, but can be trained to tree form, and get to be about 16' tall when mature. We had one in upstate NY, and it was very hardy and easy-care. Ours got only about 12' tall, probably due to the harsh winters.