The Howard Johnson is not in a good location and IIRC has no pool. There might be a few outdoor tables for drinks and food. There is a lounge for coffee, newspapers, but it does not offer breakfast or evening appetizers.

Shanghai is obviously a big city. Not many hotels have outdoor areas and many of the pools are indoor, although I recall several hotels in the French Concession area that are set in gardens, although not any associated with the brands you list. The new Peninsula on the Bund also has some outdoor space, but it is quite expensive.