There is a difference between a manual camera and one that is fully mechanical. As you can have fully manual cameras that have electronic shutters. i.e. they still need batteries to operate to their full potential.
From your post, I think you mean that you wish to buy a mechanical camera - one where the shutter mechanism doesn't require a battery to operate.
The only new Nikon FM series camera available now is the FM10 (which isn't really a Nikon but a cheap Cosina - not that there is anything wrong with that). The rest have been discontinued and you will be hard pressed to find one new in box in Singapore. But someone posted that he could still find NOS FM3as and FM2s in Indonesia.
You can pick up a mint but used FM2 from Ebay or BnS for not very much money. Plus you have a variety of other camera brands and models to choose from. e.g. OM1, Pentax K1000, etc.
Another alternative to 35mm SLR cameras is the Rolleicord Twin Lens Reflex and it's Jap clones like the Yashicas, Minolta Autocords and Ricoh Diacords. These are fully mechanical and most don't even have built in meters. These are Medium Format cameras with fixed lenses which will give you larger negatives, thus better resolution over 35mm.
I'd stay away from Seagull TLRs (even though you can still get them new) as their reliability is very questionable.
Wow, Now you look for these type. 20 yrs back very common. Now considered rare liao. Try 2nd hand shops.
Brands that were fully mechanical:
Cosina S1, C1
Practika (East German Brand - Very Solid in build)
Olympus OM-1, OM2n
Yashica FX-3 Super 2000
Ricoh KR10, KR5, XR-1
Asahi Pentax LX, (K1000 - Basically a rebadged Cosina)
Canon FT -1
Some European Brands:
Dixon - Basically a rebadged Cosina for the European Market
Phoenix P1, P2
Miranda - Basically a rebadged Cosina for the European Market
Vivitar V2000 - Basically a rebadged Cosina for the European Market
Zenit 122 (Russian SLR)
Phenix DC303 - Rebranded Minolta (China)
I would recommend getting a used but mint condition FM2 instead of the FM10. A used FM2 will cost the same as a new FM10 but is a much better camera all round. The fully mechanical FM2 is a camera that you will be able to pass down to your grand kids (as long as you don't stick your finger into the shutter).
You don't have to use the meter on an FM2 by removing the batteries. If you are worried of batteries running low, you won't have to worry with the FM2, the batteries last a long time in the camera.
A mint FM2 will set you back about $350-450 on ebay or BnS.