I'd highly recommend starting your own software company. And I'd highly recommend traveling around the world. I've been doing both for the better part of 10 years. At the same time.
So my advice is to do a quick search & replace on your question. Switch "or" for "and", turn it into a statement, then go do it.
Also, do you think having such a lifestyle can have be called as truly financially independent?
In the meantime, here's a quick overview of what I've been up to since I started working from the road:
http://www.expatsoftware.com/articles/2006/12/getting-it-dow...
From a financial perspective, it's completely counterintuitive that traveling is actually a lot cheaper than staying at home. But if you think about it a minute, it starts to make sense. Imagine you cut your rent and car payment down to zero (by ditching both car and apartment), as well as all the little bills that went along with them. Now replace that with the comparatively small expense of staying in $5/night accommodation, and otherwise living on about $20/day.
When I was planning my first long trip, taking the $2,000/month "keep life in the US alive" line-item out of the spreadsheet extended my $10k budget from 2 months to 10 months. Bill a day per month, and yes, you're pretty much set for life. Of course, you're only set for life if you don't plan on coming home, so it's probably best to leave a bit in reserve for when you do.
Out of curiosity, are you writing software or managing programmers remotely? I tried traveling and working as a consultant but dual screens and comfy chairs don't do well in a suitcase.
For western european hostels budget about 16 euros per day. It used to be closer to 8 but the supply of budget travelers has increased sharply in the last decade.
South America is more realistically $25/day all in. SE Asia, as mentioned is about $20. Indonesia is more like $10. Africa is free.
I always feel like the lack of a universal healthcare system in the US discourages lots of people from pursuing a startup full-time.