Brenjay, I will address some of the questions in your last post.
Will probably take in the area we are staying, and maybe try to hit one site close by wherever we stay.
Lodging suggestions/area's welcome."
Do you have any neighborhood scoped out which appeals to you?
Do you want a hotel room, B&B, or apartment?
Tower of London then Thames cruise
The Tower of London has an excellent lunch room, The Armories Cafe. They serve plate lunches, sandwiches, salads, desserts, and pastries. I'd suggest getting something there for lunch after you finish touring the Tower of London. It is inside the Tower of London.
For your cruise on the Thames, you are perfectly positioned once you finish touring the Tower, to go to the nearby Tower Pier and hop on a Thames Clipper boat., which take the Oyster card as a form of payment. Just tap in. The boats travel east on the river to Greenwich, and west to Westminster Pier, near Big Ben, Parliament, Westminster Abbey.
"Tour Westminster, stay for Evensong (not sure if this is every night, and I believe I need advance tickets?)
Maybe Picadilly Circus or Harrods in the evening Hours?"
I believe you do not need tickets for Evensong. If that has changed, I'm sure someone will jump in and correct me.
Especially if you have just paid to get into Westminster Abbey. If you stay that long, just take a seat in one of the pews and wait for Evensong. Westminster Abbey has a cafe for sandwiches, snacks and refreshments; so you could grab something to eat after you've toured the Abbey, and to kill some time while waiting for the Evensong to begin.
Piccadilly Circus is a busy traffic intersection. Not much to see there but traffic and some neon large advertising signs. You will go through there on a Hop-On-Hop-Off bus tour if you take one, or on one of the regular city buses used for transport around London. Skip Piccadilly Circus and go to Harrod's and get that over with.
Side trip to Stratford and Warwick Castle, doable? Worth it?"
It is do-able. You would take the train out of London, get off at Warwick to see the castle, get back on the train and continue on a very short distance to Stratford-Upon-Avon. Warwick Castle will take half a day, Stratford-Upon-Avon can be done in half a day. Train back to London in the evening.
When checking train schedules or buying train tickets, refer to Stratford-Upon-Avon by its full name. There is a Stratford in England, but it is not the same town.
You asked, "Worth it?" My opinion is that both are worth it.
tea somewhere fun?"
The British Museum has a cafe which serves a great tea. This way, you can take a break from looking around the museum, have tea, then resume seeing the museum.
I'm sure others will chime in with great suggestions for tea around London.