My fist choice route is via Spruce. It is popular with cyclists of all types, has water at the top, and takes you to within 2 blocks of the northern end of Grizzly. Wide lane provides room for bikes, and drivers are used to seeing bikes. Claremont route uses 2 bike boulevards (Milvia, Russell), or you can take Tunnel Road from the same starting point. Centennial route is for masochists and mountain goats.
via Spruce 3.1 miles, +635 feet Recommended Route
Via Claremont Drive 4.4 miles, +1,140 feet
Via Tunnel Road 7.1 miles, +1,310 feet
Via Centennial Drive 3 miles, 1,070 feet - very steep!