The downtown area is typically safe, but I still wouldn't walk around alone at night. There are several one-way streets, which can make driving confusing even for those of us who live here, so I would recommend investing in a good street map. Street parking is free after 5PM, and there are several ramps downtown, but expect to pay about $6-8 to park in one.
Winters in Grand Rapids can become quite nasty because of the lake effect snow. Snowstorms can roll in in a matter of minutes and blanket everything in white.
Be careful driving and dress according to the weather.