Tree Respawn (plants a free seed when you remove a stump)
Clock Mod (adds a display that shows in-game time of day)
Instant Monster Drop (no more delay before dead monsters pop)
Show Plant Progress (HUD of % complete when mouse-over growing plants & trees)
Trash Items (adds a delete item button to the inventory)

^-- those will not be immersion-breaking

The following mods I recommend for after you have finished vanilla, as they add content and functionality, --- v

Epic Loot (adds enchanted and unique loot, enemies can drop equipment now)
Better Wards (adds elemental wards that can damage enemies, repair structures, and heal)
Safe Death (adds option for player death to have no skill loss, keep inventory, keep buffs)
Teleport Everything (metal/eggs can now be teleported)
Mass Farming (shift+click plant a 6x6 grid, or harvest the same size in one shift+click)
Farm Grid (hold shift to see a HUD grid, that perfectly spaces trees & crops)