Two of the heavier 7'6" St. Croix from above can do that, the Daiwa anything over 15# will be sporty I'd imagine.
Lure weight (or sinker + bait description) and # test fishing line?
Around $100
For tossing those 3/4-1oz swimbaits, spoons and plugs, I'd probably go for one of the lighter 9', you could do a heavier 10' if you are going to castnet/sabiki/buy bait and use a sinker. The shorter options don't have the crazy long surf rod handle, and it's a Penn so probably easier to source for you than some local Florida brand.
They're only two piece but anything 12' and under I would expect can fit easily in a 6'4"-6'6" shortboard bag.
The PENN Battalion Surf rods provide strength, performance and style. Composite blanks, Fuji® aluminum oxide guides, Fuji reel seat and our tough and tacky rubber shrink tube handles provides a secure grip whether wet or dry. The Battalion Surf is a perfect match for PENN Spinfisher and Battle...
www.pennfishing.com
If the surf rods are too much, 3 piece Okuma SST look like a good option. I am not sure what makes it a salmon/steelhead rod but the # of pieces, length, and lure/line class looks like a good bet. They have a 7'6" that's lighter than this one:
Amazon.com : Okuma Fishing Tackle SST-S-863MH SST Travel Graphite Salmon/Steelhead Fishing Spinning Rods : Sports & Outdoors
www.amazon.com