Key West is a tourist trap.
If you like drinking go for it.
The prime and best things in the Keys are fishing, boating and diving/snorkeling.
The only good beach on the Keys is at Bahia Honda State Park.
The east and west costs of Florida have miles and miles of wide sandy beaches, but you won't find that in the Keys
With that said; yes Jan and Feb are the two best months to visit Key West or the rest of the Keys
We winter in Key Largo and love it since we are hard core kayak paddlers and there are so many good options for that.
Jack L
Jack & Nanci