Peter4

Martian -

By "the city", I assume you mean Bangkok.

Copy shops in Thailand are a different sort of business than Internet cafes.
There are many copy shops here, but most just make copies and do photo processing, and are unlikely to offer computer printing.
So, for your computer printing, look for an Internet cafe instead of a copy shop.

Internet cafes come in two varieties:
Those crowded with young boys playing computer games.
Those without boys playing computer games.
The latter kind will be able to print anything from your computer.

Their printer may be a cheap, slow, inkjet.
Or it may be a decent laser printer, perhaps even a color laser.
Either way, the cost per page will be just a few baht.

Internet cafes with printers are everywhere in Bangkok that a foreign visitor is likely to go.
Every 4-5 star hotel has a business center, but rates at those are 5-10 times higher than the independent cafes outside.
You will find more reasonably-priced Internet cafes in all shopping malls, near every university, and throughout the business areas (such as Silom-Sathorn).

One to recommend?
With the horrendous traffic of Bangkok, the one to recommend (of just about anything), is the one closest to your location.
If you don't see at least one Internet cafe near your hotel, well, sorry, but you have made a bad choice of hotel location, and not just for that one reason.

Worst case: Get on the skytrain to Siam Square station.
There are dozens of Internet cafes in the streets between that station and Chula University.

If specific questions, you are welcome to send me email or private message.

Side note:
In some areas of Bangkok, Internet cafes are used during work breaks by the neighborhood go-go dancers.
At break time, some of the dancers walk right from their dancing stage, around the corner or across the street, into the nearest Internet cafe.
If you are there trying to do serious computer work, that can be a distraction.

-- Peter