The Windy City = Chicago
Birthplace of Jazz = New Orleans
“Remember the Alamo” = San Antonio
The cheesiest city (according to Jack) in Mexico = Monterrey (Monterrey Jack cheese)
Carnaval = Rio
A poet's favorite Irish city = Limerick
The UK's finest glass cow = Glasgow
The slowest city in Norway = Oslo
Someplace I can get a good hamburger = Hamburg
Somewhere with some sites to See = Vatican City (Holy See = Vatican)
An absolute banger of a city = Bangkok
10.8231, 106.6297 = Ho Chi Minh City (Coordinates)
A certain lump of koalas = Kuala Lumpur
The 北 Capital = Beijing (The North Capital = Beijing)
Alleged birthplace of the COVID-19 virus = Wuhan
The end of the Yangtze = Shanghai
tHe Key place i plan to visit = Hong Kong (H and K are the only letters capitalized = HK = Hong Kong)
Then, from here you just have to notice that by plotting these cities on a map, they create Braille letters if grouped by the year listed (2021 = T, 2022 = A, 2023 = I, 2024 = L, 2025 = O, 2026 = R).
This is keyed in by the name of the puzzle, Blind Guess. The flavortext "route does not matter" attempts to clue in that you shouldn't draw lines between cities but instead dot.
This gives the letters of the answer TAILOR in chronological order.