How can I read a reel-to-reel tape from the 1970s?
If the tape is DECtape, you will definitely need to find a TU-56 drive to read it. TU-56 units are going to be pretty hard to come by, and would likely require some repair (replacement of old capacitors, decaying wiring, burned out indicators). As far as hosts go, you are way more likely to find a working vax than a working pdp-8, but you will need the right interface board (likely Qbus for the smaller vaxes). The bit density is fairly low at ~350 bpi and the signal is manchester encoded, so if you can get the data some other way you could certainly put it into an emulated pdp or vax (see simh-vax, works very well: simh.trailing-edge.com/vax.html). If you are very hard core you can build the interface card yourself: http://so-much-stuff.com/pdp8/cad/projects/boards.html . For more info on the TU-56 drive: http://www.pdp8.net/tu56/tu56.shtml . All of this is a lot of effort for ~184 kwords of data. You may want to try comp.sys.dec to see if anyone has any tu-56s laying around, and I certainly second the recommendation of contacting a computer history museum.
Dectapes are easily differentiable from standard open-reel tapes as they were 1-inch wide and the reels were maybe 4-5 inches in diameter, and the flanges were maybe a half-inch deep.
Dectape was one of the most robust media of its day, if not THE most robust. It had redundant timing and data tracks and could be read or written in either direction. The salesmen used to wow potential customers by punching the tape —multiple times!— with a hand held paper punch and showing that the tape was still readable. Told to me by one of the salesmen: After the paper-punch demo, a customer asked if it was water-proof, too. The salesman told us that he had had no idea but for the heck of it, he had dropped one into a bucket of water, and took the customer to lunch. When they got back, he said, he'd hung it on the drive and read it —successfully!— while water streamed off of it in all directions.
It didn't need any sticky markers —the timing tracks had all the position information it needed— but you will need a Dectape drive, and one or another DEC machine to run it (unless you're up for the challenge of building an interface and writing the low-level tape drivers for it).
Unfortunately the tapes have probably degraded past the point of recovery. The upper bound on magnetic media lifetime is 30 years:
http://www.clir.org/pubs/reports/pub54/4life_expectancy.html