You can park in Handbridge for free and walk over the bridge to the city centre. Otherwise, not much choice. The car park near the bus station is free after 3.30pm and there is some free parking by the river near the park. Those are the places we usuallu use.
I often go to Rhymetime on a Wednesday morning - tomorrow I will wear my mumsnet scarf and wave a large pom bear about, try to work out who you are! (However, I go on the bus or I park in Tesco and buy £25-worth of stuff for the free parking. If i really must use a paid carpark, the market is my one of choice.)