Google street map will be your best friend for any form of parking for any occation, make good use of it, I do, You can zoom in on the parking restriction signs in each road you go down so you don't get caught out, Believe it or not the area around Kew Gdns (not the Kew Green Area) contains many roads with only a 1 hour day time parking restriction Mon-Fri, it will also work out the walking time to get to BCS if you want, I walk from Kew Gdns station in about 20 mins at a moderate pace and I'm nearly 80, best to pre view it on a PC or tablet at home as you get a better all round view, then just use your smartphone if you have one, in the car, I am sure you will find somewhere to suit.
The only problem with this is that Google Streetview can be a bit old. For example, the nearest part of Wellesley Road to BCS opposite the Leisure Centre (zone SH) shows signs with "Resident Permit Holders Only, Mon-Fri, 10am to Noon" on Streetview as the photo is from July 2019. Lots of newer CPZ restriction since then unfortunately. This map from Hounslow BC should show the latest info:
Hounslow BC CPZ Map
Ealing have a similar map here.