I am planning to check out the War Rooms and am curious about the best site to choose. Are they located in Westminster Abbey or near it? Do I need separate tickets for both?
Definitely separate tickets. Here's the website for the Churchill War Rooms:
The two sights are very close to each other. Google Maps says they are about 1/5 mile apart. However, these are both time-consuming sights, so be sure to allow enough time in the area to see them.
as acraven says.
There is no relationship between the two places, other than that they are physically close to each other.
If your trip is early June be aware it’s the Platinum Jubilee. https://www.royal.uk/platinum-jubilee-central-weekend
Yes you need separate tickets for both The walk from one to the other is about 10-15 minutes.
Tickets for the War Rooms are timed tickets.
War Rooms hours are: 9:30am - 6pm.
Tickets for Westminster Abbey;
Absolutely pay attention to the Abbey’s event schedule.