Is there a simple way that will let me transfer all my mods setup via the NMM from one PC to another or do I have to download and install everything manually again?

Copy the data folder?

Well NMM on the new computer recognize all the mods if I do it that way?

If you're running Windows 7, for example, the archive files you downloaded for each mod should still be in Games/Nexus Mod Manager/Skyrim/Mods and you can just copy those over to the new computer. Then just re-download and re-install NMM, and put the archive files in the right folder - then install using NMM.