How about "...在海旁边"?
I'm not a native speaker or a great speaker at that, but I've always heard 海边 and not 海旁边. Perhaps 海旁边 is grammatically correct but just shortened to 海边? I think this is a good question, and would be interested in an answer too, if anyone knows it.
"旅馆" is also accepted for "hotel".
Would any native English speakers (like me!) interpret this as "near the sea", or are people generally in agreement that "by the sea" implies directly next to the sea?
Wouldn't it be better to be 是在海边 for the "is?"
No, 是 is not required. Unlike English, a verb is not always needed.
在 is a verb here: "to be located" ;)