The Baptist Church in Victoria Road South
(halfway between the railway station and the public library)

offers coffee, tea and light lunches such as soup and roll or a pizza with a choice of sweets
or again a toasted tea cake at very reasonable prices in pleasant surroundings.

It has my personal recommendation.

Opening hours are 10.30 - 1.30 Tuesday - Friday.

Their website is
http://www.findachurch.co.uk/churches/tl/tl70/cbc/