You could go anywhere OP, pretty much everywhere is dog friendly nowadays, so try and look for somewhere with the amenities that stand out to you.
I've been to caravans with the dog on my own, or now as a family we mostly stay in cottages (now three dogs too), I normally find them on Sykes or cottages.com as you can specify dog friendly, areas, facilities (like coastal) etc, sort them into price order and just scroll through till you find ones you like (or you can do 'map view' and see them on the map of the UK), just check they have a secure garden and have a read of the reviews, Anglesey & Northumberland are favourite places of ours, but Lincolnshire is fantastic for miles and miles of continuous beaches, and is the most local to us so we tend to go there.
If you don't feel comfortable being in a cottage on your own, you could look at caravan/chalet/lodge, that's what I used to do more of when I was solo with dog as it felt more comfortable, pretty much all haven sites accept up to 2 dogs, if you go out of school holidays they are cheap, or you can go on a site like ukcaravans4hire and look for a private rental on one of the sites, they tend to have more features, like wraparound verandas (unlike the standard dog friendly site ones) so you can sit outside if it's warm without tying the dog up or worrying they may run off!
Our dogs are sofa hogs, so we always take about 6-7 blankets with us to completely cover any furniture, so we can relax.