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 - £100
Big Mushroom - £2500
Nugget - £5000
Pretty Wing - £100
Stardust - £1000
Star Piece - £4900
TinyMushroom - £250

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