I only know Miri's bus station...and the enormous shopping centre next to it. However if you look hard, or even without looking too hard, you can get to Hawai Beach, walk around the park in the east of the town or even go to Lambir Hills National Park. So there are things to do...
But Miri is also somewhere you have to go through on the way from Kuching to Kota Kinabalu if you are going by bus. The day before we had travelled as far as Bintulu and found a room for the night there. Early in the morning we got on the bus to Brunei again, intending to spend the night there. Although it didn't take long to arrive in Miri we had 7 hours to wait between the two buses. The shopping centre on the other side of the road was more than enough to keep us occupied, in the cool - which was very nice considering how damp the rainy season atmosphere was.
On the whole, there are lots of better things to do with your time during your trip to Malaysia than getting to know Miri better. Don't hang around there!