Open. Whether your water is suitable can't be answered by anyone here. It just depends on the amount and type of dissolved solids that are in your tap water. Where I live it's not usable, but many places have fairly clean tap water.
Just fill a few 5 gallon buckets and let them sit out uncovered. When you use one up refill and start with the next one. I've never had to deal with city water cuz I have a well, but you'll be fine letting it sit out over night' chunk
You might want to buy a PH testing kit. I thought my tap water was fine only to discover it sits around 8.0 PH balance wise..reason why i was initially having problems with my plants. Ph kit fixed it.
It's really impossible to say if "tap water" is OK or not, depends on your tap water. Most likely it's OK, best to filter it then let it sit 24 hours. There is no specific pH that is "right" for the input water for all grow ops, you need to measure the runoff pH, which is the interaction of your water, nutes, soil, amendments, etc, and more specifically is what your roots are actually experiencing. So whatever your input water's pH, if the runoff pH is too low then you need to raise the pH of the input water, and vice versa.
I don't live in the city and my water taste pretty good we are not far from the source maybe a quarter mile. I used it at first and just let it sit over night and my plants did not grow good at all. so I got a GH testing kit for 17 dollars and the water of my PH is 8.5-9 out of the tap. here is a link to the kit Sunlight Supply, Inc - Horticulture, Lighting, and Indoor Gardening Wholesale - General Hydroponics pH Control Kit