Alphabetically
Missing letters are H,Q, U, W and Z so perhaps I should try and find a trip including airport codes that start with these letters

UVF sounds nice- Z I've technically done as the bus station at Birmingham airport has the IATA code of ZBC , Q is tougher and H looks very easy
ACA Accapulco
AMS Amsterdam
ATL Atlanta
BFS Belfast International
BHD Belfast City
BHX Birmingham UK
BOS Boston
BTV Burlington VT
BUR Burbank
BWI Baltimore
CDG Paris
CFU Corfu
CHQ Chania
CLE Cleveland
CVG Cincinnati
DEN Denver
DFW Dallas
DUB Dublin
EWR Newark
FLR Florence
FRA Frankfurt
FUE Fuerteventura
GLA Glasgow
GCI Guernsey
GCM Grand Caymen
GOT Gothenburg
GRO Gerona
GVA Geneva
IAH Houston
IBZ Ibiza
IDA Idaho Falls
JAX Jacksonville
JER Jersey
JFK New York JFK
KNX East Kimberley Regional Airport, (Western Australia
KOS Kos Greece
LAS Las Vegas
LAX Los Angeles
LCA Larnaca
LCY London City
LGW Gatwick
LHR Heathrow
MAN Manchester
MCO Orlando
MEL Melbourne
MIA Miami
MSP
NCL Newcastle UK
ORD Chicago
PER Perth
PHX PHoenix
REU Reus
SEN Southend UK
SLC Salt Lake City
SNA Santa Ana
STL St Louis
STN Stansted
SYD Sydney
TLS Tolouse
TLV Tel Aviv
VIE Vienna
YYZ Toronto
YVR Vancouver