Never dealt in blanks except for in my retail store, that being said, if I were in the business of dealing blanks, I'd market as follows:
Screen printers will be the biggest consumers of the blanks. So I would introduce myself and leave a sample with some well prepared literature. Screen printing is very price conscientious, so you'll either need to highlight your price if it's very reasonable, or produce the benefits of using you (working directly with the owner/small company, higher quality garment, being flexible). If you offer colors, washes, etc not regularly available, be sure to highlight that. Many sign shops will generally offer some form of printing/garment decorating as well, but they'll be dealing in smaller quantities, as they're generally targeting small runs.
You could try to hit some of the big box stores/supermarkets, but you'll most likely get caught up in the dreaded loop of trying to get ahold of a purchasing agent, and filling out RFPs and so on. Some of the smaller stores/chains that are mom and pop ran could probably be persuaded to buy some, but don't expect big orders from them, my retail store occasionally sells a blank shirt, but the numbers are nowhere near in comparison to what I do printwise. If things were slow and I already annoyed all the screen printers/sign shops, never hurts to stop in and ask.
If you want to go a step above all of that and get into the major orders (high quantity, low price though), you'll need to hit distributors. Your company probably isn't established enough yet to take something like this on if you have to ask the question. If you look for some of the other manufacturer's such as Gildan and who they distribute through locally, that will get you the names locally. Distributors primarily target the screen printers, they'll purchase at mill pricing and generally offload at some variable percentage depending on quantity/cases. Most distributors I've seen generally stick to about two-three brands, usually they want to be versatile enough to handle any awkward colors they might be asked for, or produce a higher quality if needed, but they don't want a million and one brands so they can master their art of selling what's needed to the printers. The guy I use in Salt Lake deals primarily in Gildan and American Apparel.
You may also want to investigate getting booths at some of the print shows if you're planning on working at this level (ISA, ISS, etc). I've never been to Magic, it's mainly a clothing line/designer wear show, but they might have something up that alley as well if you're providing a high end blank. Booths at these shows run a very pretty penny, however depending on how far you want to reach, it may be necessary at some point in time.
In short, with the information provided, I'd hit some screen printers and see if they're interested and go from there. Essentially you'll be assuming the role as a distributor. From there, you will have to decide how you want to grow. Most distributors seem to remain distributors though, they just expand, such as Sanmar, or Wasatch T (Wasatch actually started in Utah then relocated because they had much more orders coming from central/east coast). If you're planning on being the next Gildan, Hanes, FotL, etc, then you will need to target the distributors directly and start taking on more of the manufacturing road. All depends on what it is you're doing though.
