There's a page on this at
Chaz Avery's site, along with a list of venues The Beatles played in February 1962, omitting Casbah and Cavern dates.
01.02.1962 West Kirby, Thistle Cafe'
02.02.1962 Manchester, Oasis Club
05.02.1962 Southport, Kingsway Club
09.02.1962 Birkenhead, Technical College
10.02.1962 Birkenhead, Youth Club
15.02.1962 Wallasey, Tower Ballroom
16.02.1962 Birkenhead, Technical College
2nd show Wallasey, Tower Ballroom
20.02.1962 Southport, Floral Hall
23.02.1962 2nd show Wallasey, Tower Ballroom
3rd show Birkenhead, Technical College
4th show Wallasey, Tower Ballroom
24.02.1962 Hoylake, YMCA
26.02.1962 Southport, Kingsway Club