Looking on the internet deeply has found these results:

at the seaside is the most popular phrase on the web.

by the seaside 11,240,000 results on the web	at the seaside 12,570,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
And it would be a nice way for us to spend a day by the seaside. But since I'm living by the seaside It's that painting at the mansion, the seaside of Italy. In summer months the situation becomes unbearable, especially at weekends, when the road is completely paralysed by the traffic congestion caused by people travelling to/from the seaside near Rome. But if you want to know, l was born by the seaside in Whitstable, where the oysters come from. But since I'm living by the seaside I should take up painting. Nothing better than an afternoon by the seaside. Since I live by the seaside, maybe I should try painting.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

by the seaside

11,240,000 results on the web

at the seaside

12,570,000 results on the web

More popular!

And it would be a nice way for us to spend a day by the seaside.
But since I'm living by the seaside
It's that painting at the mansion, the seaside of Italy.
In summer months the situation becomes unbearable, especially at weekends, when the road is completely paralysed by the traffic congestion caused by people travelling to/from the seaside near Rome.
But if you want to know, l was born by the seaside in Whitstable, where the oysters come from.
But since I'm living by the seaside I should take up painting.
Nothing better than an afternoon by the seaside.
Since I live by the seaside, maybe I should try painting.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.