Is location important for a bootstrap web-based startup?

Sounds like you can build the site and bring along remote technical help; none of which requires a particular location. What you haven't mentioned is sales. If you need help in this area, it will be difficult to manage remotely especially if you don't have expertise in this area.

Since you asked about being in the USA, is this the market you are going after? B2B sales are competitive.

I hope you grow the business to the point where you have to consider funding.

I think location is important when you need certain skills and for some cities that attract a large number of VCs there is more funding for start-ups, as you are more likely to know someone that knows the VCs, so the local network becomes important.

But, if you are able to do everything yourself, then there is no reason to move. I think over the next few years (perhaps sooner) Silicon Valley will start to disappear due to the budget decisions, and the cost of living there.

There are many other places in the US that are good incubator cities, but, again, these are good for having help for those that need it.

If you truly can do everything yourself, you could be in the middle of the Pacific ocean with a T3 line and you would be fine, IMO.

I recently attended a lecture by Greg Gianforte, founder of Right Now Technologies and he answered this very question with a resounding "No".

Check out his lecture for more details: Boot Strapping Montana

Living outside the Valley and even the US, I would suggest that what may be different there is the certain vibe that it has attached to it. I think Paul Graham nailed it either in the article linked above or in this one. The environment is what's different. However, if you have a strong will, dedication and determination, you can do it anywhere. It's just that it's easier to get into and stay in a game that everyone around you is playing.

Location is always important. But mostly not important enough to warrant moving yourself and your family to a different country.

To estimate how big an impact a better location would have for you is almost impossible. It comes down to hov 'lucky' your future self would be in making use of the options provided by the location -- the business networks, the people, the corporate partnerships, the financing. Quantifying this can be near impossible.

I do not need mentorship

Mentorship from people who are smarter or more experienced than you is always good. Maybe you don't need mentorship, but the right mentorship could still be good for you.

to work with remote engineers while the business will be growing

That can be a feasible choice. In my experience, it always leads to longer time-to-market. This can be acceptable; but my own thinking based on my experiences is to get people as close together as possible, and move faster -- fail early etc.

real advantage of moving the company to the Silicon Valley?

Without ever having worked in the Valley, I think it's the worlds best place for extreme-growth companies, i.e. companies that hope to grow massively in value in a short timeframe. Is your business idea of this kind? If not, I personally think that less prominent startup cities can be a perfectly fine choice for most startups.

Maybe there is a middle ground? You don't write where you are located now, but most areas of the world will have 'hotter' and not-so-hot technology areas / cities. Maybe you could benefit from moving to a different city, but still staying in your own country / culture?

This fine article by Paul Graham was linked from the other recent location discussion. If you haven't read it, you should IMHO. Amongst other things, it presents a good shopping list of what to look for in a good 'incubator' city.