If you’re thinking of Ireland (not in the U.K, different currency too) you might want to post on the Ireland forum to see how you might spend a day/couple of days.
Like others I don’t think you have enough time. Consider time to get to the airport, check in time, flight, getting to overnight accommodation then the return journey. Much better to do a day trip by train. Lots of options.
As to what sort of accommodation it depends on budget, what level of service you want and whether you want to prepare your own food.
Have you booked your flights yet?
That way you do pre clearance here which, I am told, makes the process a lot easier as you arrive home as a domestic passenger.
You can't see Ireland, but Dublin might be possible.
You could consider Liverpool
2 hours by train from London
Train drops you off in the City Centre
Which is small and compact enough for you to walk around quite easily
The Pier Head
The Royal Albert Dock
And many other attractions
An early start andca late evening train back would give you a very enjoyable day
Oh and there are some Beatles stuff too but Liverpool is much more than the Beatles these days
What do you want to get out of a trip?
The ambience of what a place has to offer or a whistle stop tour to say you have visited??.
Your 9 days will effectively be less by the time you allow for the arrival and departure arrangements.
London and surrounds can indeed take up all that time and remembering that it will be getting dark quite early so the daylight hours for actually seeing things will be considerably less.
Post 1,2 and 4 are suggestions worth considering if you indeed want to get something out of the trip and minimise the back and forth travelling
I wouldn't visit Ireland in November. Its major attractions (to me) are outside Dublin, and with only 8 hours of daylight and predominantly wet and windy weather, you won't see too much of it. Same goes for the UK countryside in November - stick to cities/towns.
If basing yourself in London the following cities are all easy day-trips by train:
Do a little googling and you'll have plenty to choose from
Windsor is also an easy half-day trip.
I wouldn't schedule more than 3-4 such trips in 9 days (I assume 2 of those days are arrival/departure days).