Can't help you with the Kitsap area buttt...
The Marksman on Canyon road near Puyallup has a pretty good rental selection and well as a indoor range(one time range safety class $10ea, $11 range fee, $12 each gun rental)) (You must purchase their ammo to shoot their rental guns) http://www.themarksman.net/
Bullseye has a rental selection and range, however the range use to be a bowling alley and the acoustics are far from good. It's not the place I would suggest taking a newbie, esp if its crowded. ($5 range gun rental & $8.50 range fee) (You must purchase their ammo to shoot their rental guns) http://www.bullseyeshooter.com/rangemain.htm
Nice range, great for 1st time shooters. Range Fees: $12.50 first shooter on lane $10 additional shooter same lane. Gun Rentals: $7 one Gun, $9 all guns one caliber, $14 all pistols, $17 all guns including rifles (You must purchase their ammo to shoot their rental guns)
I am in no way affiliated with either gun range