Hyak or summit east is closed for the rest of the season so its game on for hiking, you most likely wont be alone ether. The rest of the areas at the summit are still open certain days so they will be out with snowcats and such and dont really like the public in the way. Just past the summit on the east side is the Gold Creek Snowpark which is open to public access all year. Across the street from alpental is some gnarly terrain you can hike to, i wouldnt suggest that area unless you are with some expert back country people
If you drive up to stevenpass, on the north side of the hwy behind the garage there is a trail that leads up to a couple cell towers. Just riding the road is fun enough to be worth the hike.
I'll say the same thing as the rest of these people, anything that is outside of an operating ski area is back country terrain and needs to be treated with much respect. Slopes that you are comfortable with at the ski area needs to be treated with caution when it is not controlled. My advise is to find a partner who does have experience. A small problem when you are alone can turn really bad quick. Just hand out at the parking lot / trail head and ask someone if you can tag along. A lot of people hike hyak with there dog and ride the mellow stuff. Over the summer do some reading take some classes (rei often holds free seminars) about avalanches and safe backcountry travel to better prepare your self for future outings.