Just check the weather. Considering how incredibly hot and humid is it right now, outdoors in June may be really tough! What about something in the Finger Lakes in September. We got married here in the Hudson Valley in the beginning of September and the weather was beautiful! Not too hot, a little cool at night and no rain!
As for who walks you down the aisle, that's really up to you and only you. If your grandfather has been the constant in your life, then (just my opinion here) he is the person who deserves the honor of walking you down the aisle. Your father could still be part of the processional and walk in with either his wife or a female cousin or aunt just ahead of your mother.
Just from experience, you want to be surrounded by love and support in the minutes before you walk down the aisle, not any additional emotion (like an absentee father apologizing for his lack of presence). For me, I just wanted quiet and my dad, who is has a calming effect on most people. I remember him looking at me in the back of the church and telling me that this was my last chance to walk away b/c once I walked down that aisle and said my vows in front of God and our families, we were a couple. It was oddly comforting to have the conversation with my father just before walking down the aisle. I found out later that he had the same conversation with my husband earlier that morning with the same reaction.