The English sentence is unnatural. Despite the correct direct translation of the Romanian word "mare" to "sea", the correct phrasing would be "[..] go to the seaside". Alternatively, one could say "would you like to see the sea?" (despite the tongue-twister).
Ai vrea tu sa mergi la mare? Is correct.
"Tu ai vrea sa mergi la mare?" would be more like "Is it to the seaside that you would like to go?"(as opposed to the mountain or whatever) (Native Romanian speaker here)