If you're willing to live without generating the clock from a precise BPM figure, you could build a simple cheap square wave clock from a 40106.
Having said that the Arduino is a really fun platform to use for triggering/playing analogue equipment, and great for learning on.
As a start, if you're trying to trigger the SH-101 sequencer, I'd suggest using a digital output pin rather than a PWM (analogue-ish) output. Don't forget to set the pin you use as an output in your setup(). Connect the digital out to the SH-101 clock in through a 1k resistor, and attach a pull-down 100k resistor from the digital out to ground.
Once you've got that working you could do stuff like attaching a potentiometer to one of the analogue ins to set the delay between triggers, add an LED readout for the BPM, use interrupts rather than delays so you could vary the length of the triggers, have multiple outs set to different dividers… and random clocks, control the pitch of the 101 through a cheap DAC - you could go nuts.
Just to prove that the 101 sequencer will trigger from an Arduino, I built a little overcomplicated Sync24 clock divider box a while back:
Probably the cheapest way of getting your SH-101 to run at a particular BPM setting in a commercial product is to clock it from a computer or drum machine through the Dtronics MIDI-to-sync box, although I've not tried this myself -
http://www.engineersatwork.nl/dtronics/pages/midi_sync_converter_ms06.html
hth