What are the best places to sell treasure items?

Question

For example, the guy in Undella Town buys the Relic items from you. Can you get better prices anywhere else?

What about the type Gems, mushrooms, comet shards, nuggets, pretty wing, stardust and so on? Who are the best people to sell these to?

EDIT: here are the prices from PokeCenters, for reference.
Relic items - not sellable
Comet Shard - not sellable
BalmMushroom - not sellable
Type Gems - P100
Big Mushroom - P2500
Nugget - P5000
Pretty Wing - P100
Stardust - P1000
Star Piece - P4900
TinyMushroom - P250

Answer 1

Relic Items - Riches Villa (Undella town)

All gem related - Icirrus City (nuggets, comet shards, gems, orbs)

Mushrooms - Mushroom collector (Route 5)

Star piece - Traders in anville city (you get items, not cash [ only on weekends] )

Pretty wing - PokeMarts