lots of different ideas already given, I'll sum up and add some more:
Tech:
there are free and $ tools for doing graphics, and specifically for doing dungeons. Google around and check out the programs mentioned.
If GIMP is too nerdy, consider PAINT.NET, it's free and better than Windows Paint, but much less powerful/complex than Photoshop.
DM side:
I find that running a room by room dungeon crawl is slow and boring. Some folks run it better, but that style is definitely not for everyone.
That said, any location you make should be functional, having all the sites that the people using it would need. Then make it cool. Multiple layers, tiers, volcanos/waterfalls, etc. Odds are good it will also be dense. Unless you need the storage, things aren't going to be wide-spread in a facility.
Like somebody else said, get out of the dungeon. Put your bad guys in other locations than an underground facility dug as tunnels underground, with attached rooms. There's fewer real life examples of working facilities (not egyptian burial tombs) of those style dungeons, than there are of churches, castles, houses, forts, underground based (StarGate Command/norad). So get out of the dungeon, so you can use some other architectures.
Player side:
If you want nice looking battlemat-like dungeons, you're going to need to get the tools. Tiles, those DwarvenForge pieces, or some good map making tool to do your own print-outs.
If you want to hand the players a map, get some old paper (visit an art supply store for old-looking paper or "age" the paper you have), and draw the dungeon out the way the original map maker would have. If it was the original architect or somebody who took time, use clean lines and be fairly precise. If it was done quickly, just sketch it out, with less concern for proportion and exact angle. It will look authentic.
