Where is the best place to park when going to the Needlepoint?

I would say park at the waterfront and then take the waterfront shuttle (free) from the opposite side of the road to the space needle. There might be a closer option to your destination, but I won't know about it.

Seattle parking sucks

Park in front valet is worth it

Seattle ballet parking, you can walk from there

9.99 for 1-2 hours if in front of space needle..try the street parking

I took Uber