I dont know of any Radio Shacks Left. I honestly dont know of any Weller dealers around local either. Lots of places have closed. Both of the FRYS Electronics closed. but they were ghost towns for the past 3 years or so. Wish I would have caught them in their last couple weeks to see what deals they were doing.
Maybe check HRO (Ham Radio Outlet) up at 43rd and Peoria I want to say or online at hamradio.com for Weller parts.
Otherwise get part numbers off of the Weller website and then search online for what you need.
for solder you can see what Home Depot has but make sure you dont get the super sized stuff for doing plumbing. If you are doing circuit board stuff you want real thin solder so you can control the amount you put on a trace. I use 60/40 .031 dia rosin core solder. My last spool I bought was from Radio Shack oh 6/7 years ago and its still about half full and I do a fair amount of rework on stuff, projects, tinkering, RC stuff, antennas and connectors. I havent looked at Home Depot to see what they have so I dont know for sure. Solder last forever unless unless you are constantly using it or overloading your connections. Get a 1lb spool and you will probably have it for years and years. My small spool of silver solder I bought heck 12 years ago or more and I think I still have 3/4 of it or more, but I really only used that for doing battery tabs to make racing packs from loose NICAD and NiMH cells. That was nasty stuff to work with.
Get a Fume extractor also. Or work in a ventilated space and dont breathe in the soldering fumes. Those are bad bad news, silver solder fumes are worse news.
Other online places to look, Digikey.com, mouser.com, alliedelec.com, waytekwire.com, tessco.com for specialty stuff depending on what you are looking for.
Good Luck.
Radio Man