I've sat and quickly researched every team which is sad I know but I was bored.
Vaduz - Vaduz, Liechtenstein, 4th Swiss Challenge League - Unique as play in Lichtenstein cup and qualify for Europe that way, 5873 Capacity - Closest major airport is Zurich 134km
FCI Levadia - Tallin, Estonia - Qualified as Estonia Cup winners - Midseason currently 2nd - capacity 4880 - Closest major airport Tallin
Milsami Orhei - Orhei, Moldova - Qualified as Cup Winners - 9 games into season currently 2nd - Capacity 3023 - Closest major airport Chisinau 63km
Stjarnan - Garðabær, Iceland - Qualified as 2nd in Icelandic league - 6 games into new season currently 9th - Capacity 2300 - Closest major airport Reykjavík 40km
Birkirkara* - Birkirkara, Malta - Qualified as 4th In Maltese Premier League - Capacity 17500 - Closest major airport Malta International 8km
Ferencvaros - Budapest, Hungary - Qualified as 2nd in Hungarian League - Capacity 23698 - Closest major airport Budapest
Cliftonville - Everyone knows. Capacity 8000 (3000 seated)
DAC Dunajska Streda - Dunajska Streda, Slovakia - Qualifed as 3rd in Slovak league - Capacity 12700 - Closest major airport Bratislava 50km
Buducnost Podgorica - Podgorica, Montenegro - qualified as 2nd in Montenegro - Capacity 15230 - Closest Major Airport Podgorica
Siroki Brijeg - Široki Brijeg, Bosnia - Qualified as 4th in Bosnia - Capacity 5628 - Closest major airport Dubrovnik, Croatia 156km (I think)
Pyunik Yerevan - Yerevan, Armenia - Qualified as 5th in Armenia (4th were disqualified) - Capacity 2000 - Closest major airport well there's an airport in the city closest one I've heard of is Tbilisi, Georgia 291km
Partizani Tirana - Tirana, Albania - Qualfied 5th in Albania League - Capacity 12724 - Closest major airport Tirana (can fly direct from London)
Chikhura Sachkhere - Sachkhere, Georgia - Qualified as Georgian cup winners, Currently 13 games into season sitting 4th - Capacity 2000 - Closest Airport Tbilisi 148km
Petrocub Hincesti - Hincesti, Moldova - Qualified as 3rd in Moldova - Currently 9 games into new season sitting 3rd - Capacity 2672 - Closest Airport Chisinau 28km
Zaria Balti - Balti, Moldova, Qualified as 5th in Moldova (as the 4th team went bust) 9 games into new season sitting bottom (8th) - Capacity 5953 - Closest Airport Iasi, Romania 93km (163km from Chisnau)
FK Trakai* - Vilnius, Lithuania - Qualified as 3rd in Lithuania - 17 games into new season sitting 3rd - Capacity 5422 - Closest Airport Vilnius
Luftetari Gjirkokaster - Gjirokastër, Albania - Qualified as 3rd in Albania - Capacity 8400 - Closest airport Tirana 222km
Laci - Laci, Albania, - Qualified as 4th in Albania - Capacity 5000 - Closest Airport Probably Tirana no idea how far.
IBV- Vestmannaeyjar, Iceland - Qualified as Icelandic cup winners - 6 games into new season sitting 11th Capacity 3034 - Closest Airport well its close to Reykjavik on a map but it's an island so %^*& no idea how we'd get there I assume they would move it
Ujpest - Budapest, Hungary - Qualified as Hungarian cup winners - Capacity 13500 - Closest major airport Budapest
Liepaja - Liepaja, Latvia - Qualified as Latvian Cup Winners 10 games into new season sitting 4th - Capacity 5000 - Closest airport Riga 209km
Europa FC* - Gibraltar - Cup winners - Capacity 2500 - Closest major airport Malaga 136km
B36 Torshavn* - Torshavn, Faroe Islands - Finished 3rd in League - Capacity 5000 - Closest major airport no idea would likely be a chartered flight.
Shkupi - Skopje, Macedonia - 4th in Macedonia - Capacity 5000 - Closest major airport Skopje
KuPS Kuopio - Kuopio, Finland - 2nd in Finnish League - currently 13 games into new season sitting 2nd - Capacity 4700 - Nearest major airport Helsinki 380km
Ilves Tampere - Tampere, Finland - qualified as 3rd in Finland - Currently 12 games into new season sitting 5th - capacity 5000 - 172km from Helsinki
Lahti - Lahti, Finland - qualified as 4th in Finland - Currently 11 games into new season sitting 4th - Capacity 4847 - nearest major airport Helsinki 98km
Shamrock Rovers - Everyone knows - 6000 capacity
Derry City - Londonderry, NI - Everyone knows - Capacity 7,700 (2,900 seated)
Samtredia - Samtredia Georgia - 3rd in Georgia - Capacity 5000 - nearest major airport Tiblisi 278km
Folgore* - Falciano San Marino - 2nd in San Marino - Capacity 500 - nearest major airport Bologna
Riga FC - Riga, Latvia, Qualified as 3rd in Latvia, the new season started currently 5th - Capacity 1000 - nearest major airport Riga.
Narva Trans - Narva, Estonia - Qualified as 5th (4th team merged with another team) - Capacity 2200 - nearest major airport St Petersburg, Russia 148km, Tallin is 212km
Stumbras Kaunas - Kaunas, Lithuania - Qualifed as Cup Winners - Capacity 9180 - Nearest major airport is Kaunas
Bala Town* - Bala, Wales - Qualified as 4th in Welsh League (2nd didn't get a license) - Capacity 3000
Gandzasar Kapan - Yerevan, Armenia, Qualified as cup winners - Capacity 14500 - Closest airport Tibilsi 291km
Banants Yerevan - Yervan, Armenia - Qualifed as 2nd in Armenia - Capacity 6000 - Closest airport Tiblisi 291km
Balzan FC - Malta - Qualifed as 2nd in Malta - Capacity 6000 - Closest Airport Malta International
Gzira United* - Malta - Qualifed as 3rd - Capacity 2000 - Closest airport Malta International
Racing Union - Luxembourg - Qualified as cup winners - Capacity 7000 (assuming national stadium) - Closest Airport - Accessible via Luxembourg City airport and France, Belgium, Germany.
Progres Niederkorn - Qualified as 2nd - Capacity 7000 (assuming national stadium) - Closest Airport - Accessible via Luxembourg City airport and France, Belgium, Germany.
Coleraine - Everyone knows - Capacity 4500
Glenavon - Everyone knows - Capacity 4000
Connah’s Quay Nomads - Qualified as Welsh Cup winners - Capacity 1200
Runavik* - Faroe Islands - Capacity 2000 - Closest airport again no idea how we're getting there.
*Assuming the top seed qualifies from preliminary.
NOTE: This is information I researched myself and the capacity is for their home stadium. It's likely some of the games will be switched to different venues. Please let me know of any errors.
I think I'm also missing a few teams. Possible trips to all the above and maybe Andorra and Kosovo depending if they beat a bigger seed in 1st round.