The Golden Palm Resort is in Chapel St Leonards.
Best bets there are Chapel Point:
http://www.streetmap.co.uk/map.srf?x=55 ... 73217&lm=0
Problem there now is the new North Sea Observatory they have built right on the Point itself. If you look at my avatar, you'll see the original shelter which used to sit right at the top of Chapel Point. It had seats too and, being on a slightly raised point of the sea front, gave good continental reception in the summer months. You can move along slightly to the beach hut area. There is also a walk way beyond the beach huts which gives one or two reasonable DX vantage points.
Anderby Creek is your next bet, preferably up by the beach houses:
http://www.streetmap.co.uk/map.srf?x=55 ... 75792&lm=0
Notice where the arrow is. This is a tower which forms a great DX spot, up on the dunes. It's one of the many "Structures On The Edge" which the council have built recently. Most of them are towers of one form or another. Good for us radio people!
Finally, if you travel further north into Mablethorpe, the clifftop car park is good for Holland:
http://www.streetmap.co.uk/map.srf?x=55 ... 85782&lm=0
This is a pay & display car park of Quebec Road (which doesn't actually go to Quebec!) with access to a superb stretch of beach. I can recommend The Beck for an excellent carvery.
If you are having a drive around, a trip to the large dunes at Saltfleet could be useful:
http://www.streetmap.co.uk/map.srf?x=54 ... 92765&lm=0
Plenty to go on there, but at this time of year? You'll have to come back in summer and do a comparison.