I live in this area and fly around Rainier several times a year just for fun. I've only done it VFR so I'm avoiding the Bravo too. A few tips:
If you are approaching from the NW, you're probably below the SEA B airspace so take care not to climb into as you approach. Also keep your eyes peeled because some of the SEA jet routes are nearby and they won't be much above you.
Make sure to get the winds in your briefing at 8k to 12k levels. If over 20 kts, better to fly it another day because you're in for a bumpy ride and may encounter downdrafts stronger than your airplane's max climb rate. Also watch out for "the hat" If you see lenticular clouds above Rainier, it's not a good day to fly around it.
Whether to fly around CW or CCW: depends on the wind direction - approach on the upwind side. This will facilitate your climb as you approach, and ensure you're higher on the downwind side, where there there will be downdrafts. Prevailing winds are from the SW.
Just E of Mt. Rainier is a sub-peak called "Little Tahoma", about 11,200' elevation. Watch out for that and go around the outside. The dip between Little Tahoma & Rainier may be tempting, but it tends to funnel and accelerate winds.
I usually fly around it at 10k to 12k feet. Bring a pulse oximeter and monitor your O2 levels. Pressure breathing is helpful and worth a good +5% on O2 level.
Around the S side is one of the most popular trails hikers use, so you may see a bunch of people.
There's a fun little airstrip NE of Mt. Rainier called Ranger Creek 21W. It's open June through Sep and you can fly in and camp. In summer temps the DA can get 5000' or so, so plan accordingly and ensure you're current with your high DA / mountain flying.
As you complete the circle and depart, if you're going NW back to the Seattle area, make sure to get below the Class B in time. This may require flying S turns or a big circle.