you could build a direct conversion receiver, using a digitally controlled oscillator, a balanced modulator, some RF amplification on the front-end, and an audio amplifier. the balanced modulator needs to have a lot of isolation, because the local oscillator is operating at the same frequency you are listening to. this is also called "zero IF". IIRC, there were direct conversion receiver projects in the ARRL Amateur's Handbook in the mid 1980s.
EDIT: there are a lot of different ways of making direct conversion receivers that can be found on the web. just be aware that the ultra simple demodulators (like the one that has only two diodes and uses no RF transformers) do have their limitations. the other extreme (the very complex demodulators) perform very well, but use a lot of resistors and capacitors and lots of PCB real estate. the "happy medium" demodulators generally use diodes and wideband RF transformers (or JFETs instead of diodes), and depending on the circuit you choose can work well, or barely better than the super-simple demodulator. you should be able to model these circuits in LTSpice (or other spice program) and get an idea what the pros and cons are for various demodulators. if you look at most direct conversion receivers, they either have no front end, or bandpass filters for the band of interest (many you find will be for the amateur 80 meter and 40 meter bands), a wideband RF preamp, or a preselector (RF preamp with tuning).
with a direct conversion receiver, you can have a manually tuned oscillator and use a frequency counter to indicate what frequency you are tuned to. the real key to a good direct conversion receiver, is choice of the demodulator, and the local oscillator.