The free online tool can be relatively accurate. You might be able to get approved for more. The second question is SHOULD you borrow all you can? They can be a wonderful tool but what they can't tell you is, is there a loan program in existence that makes financial sense for you. There are alot of variables to consider, your income, housing needs, expenses, debt, savings & credit history. This is a reason why it's important to find a true mortgage professional that can sit with you and understand your needs/wants and see what loan products make the most sense for you financially as well as fitting into your 1,3,5,10 year plan.
As friends, family, colleagues for reccomendations of mortgage professionals they've worked with and been happy with. Find out what their areas of expertise are, get refrences, check them out online with the Better Business Bureau, Division of Banks etc. Then sit with them and interview them to see if they understand what you are looking to do and are they able to be of assistance. It's a trust building exercise but hopefully it'll assist you in finding the right professional for you and your needs.