To the North, take a horse to find something delightful
To the West, a game piece that was tight with Paul
To the South, he can't smell, although he wasn't spiteful
To the East, you might see lavadeserticus crawl
Drink and be merry while you admire the floor
Four Directions #1
Four Directions #2
Four Directions #3
Four Directions #4
Four Directions #5
Four Directions #6 (by @PotatoLatte)
I believe that you are in the
House of Dionysus in Paphos, Cyprus?
To the North, take a horse to find something delightful
A famed horse, the Byerley Turk, was one of three horses to be forefathers to modern thoroughbred racing. The something delightful is Turkish Delight seems to indicate Turkey is to the North. Per @jafe, the horse refers to the Trojan Horse, and the fabled city of Troy is believed to be in Anatolia. Thanks, @jafe!
To the West, a game piece that was tight with Paul
A game piece in chess is the Bishop, @Gareth McCaughan found that there's a pun in the word "tight": the Titus to whom one of the allegedly-Pauline letters in the New Testament is addressed was the Bishop of Crete. Thanks, @Gareth! Crete is to the West.
To the South, he can't smell, although he wasn't spiteful
This could be the Sphinx (since he's missing his nose!) in Egypt, which is to the South.
To the East, you might see lavadeserticus crawl
This is the Syrian house gecko, endemic to Syria which must be to the East.
Drink and be merry while you admire the floor
At the entrance of the house is a floor made of shells depicting Scylla. Dionysus is also a God of drinking and being merry in the Greek pantheon.
Partial and doubtful answer
I suspect you're in
Cyprus
though I haven't figured everything out.
To the North, take a horse to find something delightful
To the north is Turkey, as in Turkish delight. Not quite sure why the horse; there are horses from Turkey and horses in Turkey, but it sounds as if something more specific is intended.
To the West, a game piece that was tight with Paul
Not sure about this. Crete is to the West; perhaps there's a pun in the word "tight" since the Titus to whom one of the allegedly-Pauline letters in the New Testament is addressed was the (a?) leader of the Christian community there -- but I'm not sure why "a game piece".
To the South, he can't smell, although he wasn't spiteful
To the south is Egypt. Many Egyptian statues have had their noses removed (though presumably not "cut off to spite their faces"), for reasons that aren't perfectly clear.
To the East, you might see lavadeserticus crawl
To the east is Syria; Hemidactylus lavedeserticus is the Syrian house gecko.
Drink and be merry while you admire the floor
Not sure quite what's going on there. There are some fine mosaics on Cyprus, I guess, but again it seems like there's more to it than that.
