If you plan on going to Greenwich anyway (for example), the Maritime Museum and the Observatory are set in the middle of a park; and you can combine it with a boat trip one way and a trip on the DLR (driverless trains!) the other, and include a stop-off at Mudchute to walk in the local park and city farm there.

IMO, Kensington Gardens and Hyde Park have real attractions within them for tourists. We have walked all over them to see the Serpentine, Peter Pan statue, Italian gardens... even a quick tea at The Orangerie at Kensington Palace would be a thrill, I think, for me if I were a 13 year old girl. Heck, it's a thrill for me now. Speaker's Corner, the Dog Cemetery... I would not pick a wander through St James' Park over a visit to KG/Hyde Park.

Anyway, my two cents.

We visit parks just about every place we go. Most recently spent a lovely Sunday afternoon in the Villa Borghese.

Hyde Park is not much of a walk from The Eye being kitty corner from Green Park.>

Yes but the lures of Hyde Park, which to me are great, that you mention are a longish walk from that kitty corner tip of Hyde Park - and IMO St James Park is stunning - as good as any other park in looks and is the perfect park for what the OP wants.

Heck it could take 8 minutes just to cross the busy round-about and main streets by that tip of Hyde Park, the tip of the proverbial iceberg.

If you are an old lady who feeds birds in the park - St James's would be perfect ;)

(BTW - it isn't St James . . . It is St. James's)

My main issue w/ St. James's it is this long/skinny park w/ this long/skinny lake running the whole length and only one place to cross -- just a lot of 'effort' w/o much bang.

A nice respite from hustle and bustle - sure. A place to while away 2 hours w/ a 13 yo - nope, not IMO.

Yes janis you are right - OK?