Pre Peel apartment days I used to stay at the Pitcairn B&B, church road marina, Douglas - phone number should be available via directory enquiries - this was very friendly, very reasonably priced and within 200 yards (50 vertical! but there is a lift via carpark and bridge) of Manx Museum so I could be there on dot of 10 am.
Peel is less well served by B&Bs but there are several, but with just 3 nights I suggest you stay at one spot - obviously I recommend Peel but then you need a 30min bus ride to reach the metropolis.