Downtown San Diego and it's surrounding neighborhoods are extremely popular so parking can be tough. You will find it almost always but you need to be prepared to walk. We Uber almost everywhere when we go to the popular places in and around downtown. Little Italy - without a valet option - is almost impossible. You do have the option to park up the hill in Banker's Hill but you will have a bit of a hike.
San Diego can be unpredictable in May/ June. The closer to the coast you get, the more likely you will get fog. The bay tends to protect Downtown and Little Italy from the fog but there is the chance it could be warm and humid. Hoping for no fog but it's something to be prepared for.
The ceremony will be held at a home in Banker's Hill. A quick reception when everyone gets there and ceremony in the garden area to follow. After the ceremony, we will have time for pictures before heading off to dinner down the hill in Little Italy. The home is in a quiet neighborhood with decent street parking but, again, Little Italy will not have much to offer besides Valet on a Friday night in the summer.