heavy, stout (BrE), strong, sturdy
clumpy (BrE), clunky (AmE)
light
comfortable, sensible, soft
old, worn, worn-out
dirty, muddy
patent-leather, polished, shiny
matching
She wore a dark blue dress with matching shoes.

designer, fashionable, stylish, trendy
casual
dress, dressy (informal, esp. AmE), fancy (esp. AmE), smart (esp. BrE)
open-toed, pointed, pointy (informal)
flat, high-heeled, low-heeled, platform
buckled, lace-up, slip-on, strappy
canvas, leather, rubber, suede, etc.
boat (esp. AmE), deck
court (BrE)
oxford (AmE)
athletic (AmE), gym, sports, training (BrE)
climbing, running, track (esp. AmE), walking
bowling, golf, skate (= for skateboarding), tennis
basketball, soccer (both AmE)
dancing
ballet, pointe, toe (esp. AmE)
tap
baby

pair
a sturdy pair of walking shoes

put on, slip on
kick off, pull off, slip off
tie, untie (both esp. AmE)
lace, lace up, unlace
break in
to break in a new pair of shoes

reheel, repair, resole
I've had my shoes resoled.

buff, clean, polish, shine
scuff

fit (sb)
pinch sth
The shoes, though elegant, pinched her feet terribly.

squeak

polish
size
What's your shoe size?

shop (BrE), store (AmE)
repair
leather
company, designer, factory, maker (usually shoemaker), manufacturer
box, rack
insert (AmE), insole
For her feet the doctor recommended shoe inserts.

the heel of a shoe, the sole of a shoe, the toe of a shoe

Shoe is used with these nouns as the object:
horse, pony