Near Taipei 101, then I would first go to the Xiangshan (elephant mountain) area, which is one of the SiShoushan (four animal mountains) group, just a couple kilometers SE of 101 I think. I’m guessing a taxi ride would be $4US or so. If the company and house both provided dedicated parking spots, that wouldn’t be a bad drive either, I imagine, although others living in/close to that area may have better advice.
Note that some folks sign contracts with agents to sell/rent their place, and I think the agent charges a full month of rent EACH from the landlord and tenant for this service; at least, that was standard practice 6 years ago in my area.
I had mixed experiences with the agents; some ignored what I said about my requirements, and wasted my time taking me to unsuitable places; others were showing places that were not worth the asked price.
Note also, there are not a few landlords who post their own “RENT” sign. THe Chinese character looks like this: 租 and if it’s rent or sell, it says 租/售. If you don’t speak Chinese, you might be able to get a colleague to go with you; although it sounds easier to rely on an agent, relying on both an agent and yourself simultaneously gives you a broader choice. I did that, and ended up renting a place I found myself. I got a better deal, too.
One of the quickest ways is to borrow a scooter, and strap a digital camera around your neck. Zip around a suitable area, and when you see a nice, quiet, hopefully shaded little lane , zip in looking for the rent signs. If you see one on a nice building, take a pic of the sign (has cellphone no.) and then the address (at 1st-floor entrance) so you can find it again. (Assuming you don’t speak Chinese and can’t call the no. immediately)
After a morning of collecting these, return to the office and have a colleague or secretary call all the no’s and get more info. If any look good, then you return with a local to have a looksee.
I find this method more efficient than agents, personally, because you eliminate from the get-go any apartments on noisy streets, or too far, or which look old, or (important!) which are resting on tiny little pillars that will collapse in a big earthquake. Also avoid 1st floor apts due to typhoon flooding, as well as apt’s right next to a big hill where they’ve cut away from the hill to build it, as there’s landslide risk there.