Weekends are usually the days when most people have the time, then you can pretty much choose the time to what suits you best. If you choose a weekday, some time after 17.00 is probably better.
If you intend this to be a short meet & greet type of event, then pretty much anywhere should be fine.
Finding places with public shelters in the city centre isn't easy, but here are two downtown suggestions:
N60 24.015 E5 18.080 - Nordnes
This is in a city park with a nice view towards the sea. 15 minutes to walk from the fishmarket. Some parking nearby. Trees in the area may provide some sort of shelter against rain.
N60 23.471 E5 19.581 - Festplassen
This is a traffic-free square very centrally located. 5 minutes to walk from the fishmarket. Ample parking in nearby P-houses. A nearby cafe might provide shelter in rain.
Have a look in Google Maps and take a look at the city centre. Anywhere with trees or grass nearby should be OK for events. Obviously there are exceptions to this, but we're here to help