I spend on average about 10 days a month in hotels, i think nothing of going cinema on my own, ot the indian/Chinese/pub/club/museum/walk along the beach I actually like my own company. Go for it.
Yep, I used to do a lot of that as well, all over the world.
I've seen some amazing museums, cathedrals and castles, and a lot of films in strange places,
'Gladiator' in an Roman amphitheatre was so good I went twice (it was also the only film on the bill in English)
I've also eaten in hundreds of restaurants on my own.
The best of which, (usually in Greece oddly enough,) have a single diners table where they put you all on one table, which has occasionally lead to long evenings putting the world to rights with complete strangers.
The only place I've felt intimidated by eating alone is in Germany. It just does not seem to be the done thing there.