I'll add - if you have tires that can handle light gravel, that opens up even more trails to you (Snoqualmie Valley Trail, East Lake Sammamish Pkwy trail, etc.

Generally I'd tell you to stay off the Burke Gilman when the weather is sunny. There are too many little kids, dogs, people biking in big slow groups, etc. The I-90 trail has way less traffic - definitely check that out. It has some moderate climbing, plus from there you can ride around Mercer Island which is a very twisty / fun ride.

Edit: there's also track cycling at the Marymoor Park Velodrome if that interests you (even to spectate). They do Friday night races all summer.

https://velodrome.org/jbmv/calendar/