There are many bicycle shops in Thailand that have at least the basic equipment and inexpensive labor.  In the larger cities like Bangkok, Chiang Mai, Chiang Rai, Phuket, Pattaya, Khon Kaen, and Hua Hin there are usually a couple that offer high end bikes and parts.  Most of the smaller towns will have some place that you can buy inner tubes or get repairs done. 

Bangkok and Vicinity

BIKE ZONE - Bangkok's Newest Bicycle Shop
Location:  in the Outdoor Unlimited zone on the 2nd floor of Amarin Plaza (the old Sogo next to Erawan), BTS Chidlom (150m).  This is the only bicycle shop that is actually attached to the BTS Sky Walk.
Contact:  02-652-1559
Website:  www.bikezone.co.th
 
This shop is a full service shop located in the back of the Amarin Shopping Center and they carry Giant and Santa Cruz bikes as well as many quality accessories and biking gear.  Stop by and check it out!

Probike
Location:  237/2 Ratchadamri Rd, Soi Sarasin, Lumpini, Pathumwan

(A short walk from the Ratchadamri BTS Station - Bikes allowed on BTS Sky Train but not MRT Underground unless fold-able)
Contact:  02-253-3384, 02-254-1077
Website:  www.probike.co.th
Probike is located at the northwestern edge of Lumpini Park, Probike is one of the biggest importers of bicycles (Trek, Klein, Gary Fisher, and others) and bicycle accessories. You'll also find lots of information on biking events and routes here.

Saengthong
Location:  32/13 Pracharaj Rd, Amphoe Muang, Nonthaburi
Contact:  02-525-1789, 02-526-4664
Although located out of town, Saengthong bike shop is frequented by both Thai and foreign tourists, and specializes in mountain bikes.

ThaiCannasia
Location:  45/39 Soi Atthakrawe 1, Sukhumvit Soi 26
              (Near Carrefour/Behind S&P)
Contact:  02-253-3454, 01-332-8687, 01-567-8886
The Cannondale Center (Thaicannasia), They are the Exclusive Importer and Dealer for the full range of Cannondale Bikes, Clothing and Accessories as well as Mavic & ZIPP Wheels, Giro Helmets, the usual range of accessories and much more.
*Authorized Sweetskinz Bicycle Tire Dealer

Viwat Bike
Contact:  02-552-8583, 02-972-3934
The shop, featuring a large variety of bicycles and accessories, is located near the Honda Bangkhen showroom and close to Yaek Lak Sii intersection.

Word Bike
Location: Ram Inthra Road (at Ram Intra 75)
Contact:  02-946-4117, 02-510-1041
Another large importer (Giant and other brands) that offers a huge selection of bicycles and accessories, odd parts, and many bargains. Service is good.
*Authorized Sweetskinz Bicycle Tire Dealer

Peloton (formerly called SpinBike)
Location:  2355 Union Tower, Petchburi Rd., Bangkok
(across from the Thong Lor/Sukhumvit 55 and Petchaburi Rd. intersection.
Contact:  02-318-1669
Website:  www.peloton.co.th
Specializing in high-end road racing bikes, parts, and service.

Siam Bike
Location:  245/6 Pattanakarn Rd., Suanluang, Bangkok
Contact:  02-722-9999, 02-733-9704, 02-722-9004
Website:  www.siambike.co.th
Well-rounded bicycle shop that has bikes for all occasions.  Ranging from very high-end for pros to low-end for beginners.  Some of the bike names they carry are:  Colnago, Gary Fisher, BMC, Specialized, Trek, Jamis, and Merida.

Interbike Sales & Service
Location:  16/212 Samakee Road, Nonthaburi (Next to Nichada Thani Entrance) Open 9 AM to 7 PM daily but closed on Monday's.
Contact:  02-952-4242, 081-842-0944
Mr. Jumphot speaks English well and has a good selection of High-End Parts, Trek Bicycles, Giant Bicycles and some local bikes for kids.
*Authorized Sweetskinz Bicycle Tire Dealer


Chiang Mai

Jackie Cycles
Location:  Just off the northern flank of the moat, 100m on the left down the Mae Rim Road - signs in Thai only
Has the best selection of accessories in town, and stocks Gary Fischer, Trek, and Klein.

Top Gear
Location:  Chiang Moi Road, parallel to Thapae Road
Centrally located and sells high-end gear, such as GPS, as well as good value Merida bikes.

Chaithawat Cycles
Location:  Old Town on the southern end of Prapaklao Road
Offers good value on accessories, as well as Challenger bikes and better known brands.

Velocity
Location:  Beneath the Novotel hotel, out of town.
Rents out decent quality, well maintained mountain bikes cheaply. They also have a selection of Giant mountain (and road) bikes for sale, supported by accessories.

Cherry Bikes
Location:  Out of town on the Chiang Rai road.  It is tricky to find and they don?t carry a huge selection of bikes but have some interesting imported accessories.

Chiang Rai

Fat Free Bikes
Location: in the city center, just a few block north of the Night Bazaar and a block west of the Clock Tower at the intersection of Th. Phahonyothin and Th. Banphaprakan.
Phone: 0-53-752532
Fat Free has a wide variety of mountain bikes and mountain bike gear and great mechanics.  The owner, Bird, is an expert in routes in the area. 

Samui

Red Bike
Location:   438/7 Moo 1, T. Maret, Lamai, Koh Samui 84310 Thailand
(300 Meters South of Hinta Hinyai)
Mobile: +66 (0) 87-278-8818
www.redbicycle.org

In Pattaya, there are at least 3 shops selling new and old bikes and accessories on Thepparasit Road, near the speedway track. At least one of these sells imported bikes and accessories.

There are a lot of bicycle (and motorbike) shops on and around Worachak Road, Chinatown in Bangkok - a couple of them sell imported bikes and some with accessories but mostly only new and second hand Thai bikes.

In Chiang Mai, the Central department store on Huay Kaew Road has Star Sports which stocks various bicycle accessories, but no bicycles.

Hua Hin has a great bike shop called Hua Hin Bike.
It is located just north of town on the east side of the road.
11/37-38 Phetchakasem Road.
Ph. 032 530292, 09 8377732 ask for Cake.
They carry a good selection of road, mountain and some Hybrid bikes.
Also have a great selection of clothes, shoes and components.
Some bikes they carry are Trek, Merida, Gary Fisher, Wheeler and Challenger.
I have bought three bikes there and the service is excellent.