What is the best way to leave property to someone in an unmarried situation?

First, bear in mind that unless you are already on the mortgage, that you can't take it over and pay it: rather, when the mortgagor (person taking out the mortgage) passes away, the mortgage must be paid in full, whether by simply paying it or by refinancing it in a new owner's name. The will cannot address what happens to the mortgage, because the mortgage is a contract with the lender; the lender's rights (e.g. right to payment) cannot be affected without the lender's consent. So while the will can leave the property to someone, that person or persons will have to address the mortage on his/her/their own, unless the will also sets aside money to be used to pay the mortgage. 
There are two ways to go in terms of leaving the property: 1) the will can just leave it 50-50 to both you and the daughter--then, as an owner, you have a right to live there, use it, etc.; or 2) it can give you a "life estate" (right to live there for life) subject to you paying all or more of the monthly expenses (whatever he feels is fair) and the "remainder" interest to the daughter, so she inherits when you pass away (and you can't sell the property out from under her, because you can't take away her interest).
The pros of 1) are: it's simpler; if you and the daughter sell the property, you get half the equity. The cons of 1) are: she has an equal right to live there as you--you may have a roommate against your will, so to speak; and if you and she disagree about what to do with the property, she can force the sale of the property by going to court, at which point you each get 50% of the equity or proceeds.
The pros of 2) are that it is guaranteed that you, and only you, can live there; and the daughter can't force the sale. The main con is that since you don't really own it, just have the right to live there, if you end up wanted or needing the money, you can't get it through the sale of the condo.