Where do I find all the artifacts?

You're right, you're missing other ways to get new artifacts. According to Stardew Valley Wiki, artifacts can be acquired in the following ways:

  • Using the Hoe on worm tiles. Different parts of the map will drop different artifacts. These locations are much more common in winter.
  • Using a Hoe on dirt located within The Mines and Skull Cavern.
  • Killing Monsters.
  • Fishing for treasure chests.

In case you want a list with the artifacts and their locations, see below or refer to this page:

Dwarf Scroll I

Mines level 1-105 (maybe every level, not confirmed)
Green Slime (Secret Woods)

Dwarf Scroll II

Mines level 40-65
Blue Slime (Secret Woods)

Dwarf Scroll III

Mines level 40+
Lava Bat (Mines Level 81+)
Blue Slime (Secret Woods)
Skull Cavern

Dwarf Scroll IV

Any Monster (Mines)
Using hoe on dirt (Mines level 81+)

Chipped Amphora

Town (4%)

Arrowhead

Mountain (2%)
Forest (2%)
Bus Stop (2%)

Ancient Doll

Mountain (4%)
Forest (3%)
Bus Stop (3%)
Town (1%)
Fishing Chest (Ocean/Secret Woods)

Elvish Jewelry

Forest (1%)
Fishing Chest (?%)

Chewing Stick

Mountain (2%)
Forest (2%)
Town (1%)
Fishing Chest (?%)

Ornamental Fan

Beach (2%)
Forest (1%)
Town (0.8%)
Fishing Chest (River)

Dinosaur Egg

Mine (1%)
Mountain (0.8%)
Fishing chest (Ocean/River)

Rare Disc

Underground Mine (1%)
Fishing Chest (Ocean/River)

Ancient Sword

Forest (1%)
Mountain (0.8%)
Fishing Chest (Ocean/River)

Rusty Spoon

Town (5%)
Fishing Chest (River ?%)

Rusty Spur

Farm (10%)
Fishing Chest (River ?%)

Rusty Cog

Mountain (5%)
Mine ~14 in dirt
Fishing Chest (Ocean/River)

Chicken Statue

Farm (10%)
Fishing Chest (?%)

Ancient Seed

Forest (1%)
Mountain (1%)
Fishing Chest (River)

Prehistoric Tool

Bus Stop (4%)
Mountain (3%)
Forest (3%)
Fishing Chest (?%)

Dried Starfish

Beach (10%)
Fishing Chest (River ?%)

Anchor

Beach (5%)
Fishing Chest (?%)

Glass Shards

Beach (10%)
Fishing Chest (Ocean)

Bone Flute

Underground Mine (2%)
Mountain (1%)
Forest (1%)
Town (0.5%)
Fishing Chest (River)

Prehistoric Handaxe

Mountain (5%)
Forest (5%)
Bus Stop (5%)

Dwarvish Helm

Underground Mine (1%)

Dwarf Gadget

Underground Mine (0.1%)

Ancient Drum

Underground Mine (2%)
Bus Stop (1%)
Forest (1%)
Town (0.5%)

Golden Mask

Desert (4%)

Golden Relic

Desert (8%)

Strange Doll 1

Everywhere (0.1%)
Fishing Chest (?%)

Strange Doll 2

Everywhere (0.1%)
Fishing Chest (?%)

Prehistoric Scapula

Town (1%)
Forest (?%)

Prehistoric Tibia

Forest (1%)
Railroad (?%)

Prehistoric Skull

Mountain (1%)

Skeletal Hand

Beach (1%)

Prehistoric Rib

Town (1%)

Prehistoric Vertebra

Bus Stop (1%)

Skeletal Tail

Underground Mine (1%)
Fishing Chest

Nautilus Fossil

Beach (3%)
Fishing Chest (Ocean/River)

Amphibian Fossil

Forest (1%)
Mountain (1%)
Fishing Chest (Ocean)

Palm Fossil

Forest (1%)
Beach (1%)
Desert (1%)

Trilobite

Forest (3%)
Beach (3%)
Mountain (3%)