Try not to worry about it.
I went in last week, I didn’t give it a thought until I was walking across Westminster Bridge. Even then it was just a ‘how sad for those families’ 😢
Just make sure you have a map and a plan. London is only small but unless you know your way around you can walk a lot & not see what you want to.
John Lewis is well worth a visit, their windows are (nearly) all the Monster from their advert and a Monster house (free) on the 4th and you can go up to the Garden Rooftop on the 6th floor, fab views and a good space for the kids to let off a bit of steam. Nice cocktails too!
The Carols in front of the huge tree in Trafalgar Square are lovely and no more of a risk than anywhere else.
You don’t need to get the open top bus, just take a regular bus (kids under 11 free. Over 11 is free too but a bit off a faff as you need a photo Oyster card. One day, I’d just pay. There might be another way, it’s not something I’ve needed).
South Bank market (along from the London Eye) is nice this year, make sure you go into the Reorderling Cider bit, there are a few stall & several with food. The entrance is misleading as it looks like it’s ONLY a Cider Bar, it’s not. There are some lovely wood burning, warming, fire boxes in there - it was lovely.
There is too much to enjoy, not to go, for the 1/billion chance you’ll be in the wrong place at exactly the moment some fuckwit does something dreadful.