The Beaches (Atlantic/Neptune/Jacksonville beach) are very nice, I agree

.
But housing is limited at the beach simply because there is not much land. It is not that deep of an area (I want to say 2-4 miles deep? And about 6 miles long?). So there is only so much land and once you go beyond that, you're "off beach" (locals refer to is as "crossing the ditch" with 'the ditch' being the Intracoastal Waterway).
This means housing prices are high there. A beach address comes at a premium, not to mention more expensive homeowner's insurance, etc.
You might find something you like for under $270k...stranger things have happened

...but I would expect your search to be on the challenging side. The last time I pulled a flyer on a house at the beach, it was priced in the high $600k range. And that was a late 1970's fixer-upper less than 2000 sq ft on barely any land....but it was 4 blocks from the ocean

.
You should still look for yourself and see. You might be happy in a condo, or be willing to take on a serious fixer-upper, or find some other way to live at the beach in your price range, it's worth exploring to see what's available.
if you decide to "cross the ditch" into the "Intracoastal West" area, you'd be 5 or 6 miles from the ocean (10-15 minutes drive, max). Here, you can have your pick of homes under $270k, many of which are relatively new and in very nice neighborhoods. Just crossing that waterway changes the housing prices dramatically...but, it's not 'at the beach', of course

.
You'd also be in the heart of some serious shopping, including a favorite topic of ours on the forum - the Saint Johns Town Center. Schools are generally very good at the elementary and middle school level (usually A-rated), but the high school level has some serious overcrowding that has affected the school's performance big time. One of the main high schools for the area is Sandalwood High School, which is not only the largest high school in Duval county, but the largest high school in NorthEast Florida. A new high school is in the works (opening in 2010, I believe) and will alleviate much of the overcrowding.
If you can't find what you're looking for at the beach, try the San Pablo area - it's just across the Intracoastal from the beaches and might be "beachy enough" for you

. The zip for that area is 32224. If you want to expand your search on the area, add zips 32225 & 32246.