Conch Club is located on South Hole Sound.  As such, you don't have
what most people would characterize as "worthwhile" shore diving out
front.

I was on LC last Nov/December (post IVAN), but didn't bother to do any
real scouting for shore diving ... was being lazy and boat diving.
There are some spots here and there, but they generally require you to
have reasonably good transportation to get out of the Blossom Village
area on South Hole Sound, and since a rental Jeep on LC is roughly
around $80 per day, its cheaper to just stay on the boat.

Thus said, if you want to DIY some shore diving, your best bet is
probably to be based out of Sam McCoy's on the north side...a friend of
mine stays there frequently, and IIRC, he does the Bloody Bay area from
within walking, biking and/or swimming distance.

Your other low-cost alternative from Conch Club would be to get out to
Owens Island to snorkle...either pay for the boat taxi (sorta), or walk
up towards Head 'o Bay and ask permission to swim out from their dock.

In either circumstance, do watch out for longshore currents to prevent
getting swept away & out to sea...its not really for the fainthearted
and you're a long ways from anyone who's even around to spot you
getting swept away, let alone to play lifeguard.

-hh