Just to give you an idea of potential savings: Including utilities and fiber optics into my house I pay $500/month (two bedrooms, fully furnished house with giant terrace) - the same is available online for $120/day. This is in southern Morocco and even the 500 I pay include a tourist penalty fee. Local cops start with a salary of $220/month...
The challenge we are currently facing is finding a place in the US for two-three months that's actually affordable. Even the hotels are crazy expensive for short stays.
It definitely seems like picking a city, getting there in a hotel, and then finding a place is a better strategy than finding something online. I've been to countless websites that return an error when I put in our target dates: 'our reservation system doesn't allow dates longer than 30 days'!?! LOL Then, almost everything for our target duration is 'vacation rental', which means they want at least $500 per week.
Total side note: is there a way to get notified when people respond to your comment on HN?
And thank you for the description of your process, always good to get another perspective. We find ourselves working very hard to find the proper place before we arrive, and having some local time first would definitely seem to make things easier. Just have to balance that cost with our budget.