Need somewhere to stay a sat night in Bexhill-on-Sea in June. 2 adults 2 young dc. Suggestions please!

[Flibbertyjibbet]

We are on hols in Dorset and I've decided that instead of coming straight home to Lancashire on the sat we should take a (rather long!) detour to visit dp's grandad in Bexhill.
DP hasn't seen him for 15 years and he's never met our two ds's now aged 3 (well he will be tomorrow) and 4. Plus the grandad is nearly 90 so I know its awful but I thought if we don't go this year then what if we don't get another chance?
We won't be able to stay at their small house, so am looking for a travel lodge type place or B&B.
Either in or near Bexhill, or somewhere a few hours drive in the general direction of the north west (thinking Berkshire ish?) so that we can use it to break up the journey.
Cost is a big consideration so please don't suggest any 4 star hotels!
Thanks!