I think Heaven (the new Heaven) will be laid out like a cube stretching 1,500 miles on all 4 sides and 1,500 miles high (think northern Ohio to southern Florida to western Texas up to Nebraska and back over to Ohio--that may be around the size of the New Heaven). I think there will be levels or floors to house all of Heaven's inhabitants since the creation of man. It will shine brilliantly from all of the precious stones the walls are built out of. I believe there will be 12 gates (3 on each side for the East, West, North and South walls) each made out of a single pearl. I believe there will be a river that will run down the middle of the city (the River of Life) with trees lining it bearing fruit. And of course the streets are paved out of pure gold, so shiny it appears transparent like glass. I also think there will always be songs of praise and worship to God going on everywhere that will be the most beautiful music we have ever heard. This is only the New Jerusalem that will sit on the New Earth.
I believe the New Earth will be paradise. I don't know what it'll look like but there won't be any more seas or oceans. Maybe you and I can go fishing in a pond or lake, though, because I love fishing too.
This is not in the Bible but I do believe our pets that have died will be there on the new earth some where. Maybe God will designate a huge field for all of them to play or maybe they will be in our mansion/room waiting for us that God is preparing right now for us. This is weird but I believe we might even be able to talk to them =)
That is what I think Heaven will be like--some backed up by Biblical descriptions and some what I think will be there that is not in the Bible, just my thoughts. Either way, no eye has seen, nor ear has heard how beautiful it will be. You just can't write it into words.
We will not breathe because there will be no reason to. We will be spirits. We will not have to eat either to sustain ourselves. I believe we will definitely be able to fly which I am looking forward to. And I hope, really HOPE that God will let me fly around the universe and visit distant worlds and stars. I can't wait! But then again, maybe my desires will change once I behold the Lord and I would never dream of being away from him long enough to bother exploring the universe. Maybe He will hold my hand and go with me, though. I don't know, but it will be exciting whatever happens and whatever Heaven has in store for us!