There are a bunch of options for getting across the river. You can ride across the I-5 bridge, the I-205 bridge, or you can take the Yellow Line Max all the way to the end and catch a bus across. The sidewalk on the I-5 bridge is REALLY narrow, like if you meet someone coming the other way one of you has to stop and get out of the way. The cool thing about the bridges is you can do a nice loop. I like to ride up to I205, back down Marine Drive, and back over on the I-5 bridge.
Once you're in Vancouver, there are lots of great places to ride. The ride out to Vancouver Lake is nice. The city is pretty bike-friendly, with lots of bike lanes on streets, and bike paths closed to cars.
Here are a couple of sites that might help:
The City of Vancouver's site: http://www.ci.vancouver.wa.us/transportation/bike.html
The Vancouver Bicycle Club: http://www.vancouverbicycleclub.com/
Hope this helps!