Yes, you are right. It all depends on where you are.
If you are in an inland town ( i.e. not on the coast) , you might say 'Let's go to the seaside'. And yes, this included all the facilities of the seaside resort.
I live in a town which is a seaside resort, so we never say 'go to the seaside', because we already live there. We would say 'Let's go to the beach'.
When you are already on the beach, sitting on deckchair enjoying the sunshine, you might say 'Let's go in the sea'.
As Ruthi says, 'go to the sea' isn't a normal phrase to use. You'd only refer to the sea ( i.e. the water itself) specifically if you are already at the beach. In that case you would say 'go in the sea', which means enter the water.
One more piece of vocabulary for you: in British English at least, we talk about going to the 'seafront'. This is the promenade running alongside the beach, with shops, cafes etc. - the equivalent of the Italian 'lungomare'.