You should probably think of ~100kHz as maximum for NE555 and ~500kHz for the CMOS versions (assuming suitable values are chosen for both the capacitor and resistors. Above that it starts to become very part and manufacturer-dependent. And maybe 1/10 of that if you want the output frequency to be very predictable and stable (by 555 standards).
Since the antique AY-3-8500 runs from a 6-7V Vcc it's not convenient to use off-the-shelf oscillators. But it will accept a 0/5V CMOS input if you use a 6.5V Vcc and sub regulate it down to 5V for the oscillator, using an LDO. Alternatively, there's a crystal oscillator circuit using a 4001 which I would not recommend since 4001s are hard to find (4001B is not the same) though you could use a 4007, and an LC oscillator using a 90uH inductor, both on the datasheet. 90uH is a bit large for an air-core coil, but totally do-able if you have a few square inches to spare. It will work with any general-purpose NPN transistor such as 2N2222:
simulate this circuit – Schematic created using CircuitLab