Yes, reel to reel decks or open reel decks, as they are commonly called are available indeed, but you'll have to be extremely patient and extremely lucky to find one in good condition. These are usually left stored away in lofts, under beds or in store rooms under a pile of rubbish. I have come across over a dozen of decks over a 2 year period during which I was actively searching. But the condition was generally very poor. I also was very particular not to indulge in belt driven reel to reel decks as these tend to have very complex mechanisms. Finally my wait for a reel deck paid off when a lovely forum member sourced a relatively brand new Akai GX630D direct drive deck for me in non-working but untouched condition. I bought it blindly even though I was not sure if it would work. As it turned out, it was in untouched condition and needed some minor TLC to get started which Mr. Kuruvila helped me achieve. Its a classic Akai deck, one of the more famous and well received models. Can't wait to hear it play for the first time.
Regarding tapes, I got the deck with a set of 10 tapes. You cannot get tapes for these decks unless you buy from abroad. They are expensive and heavy so importing will incurr significant shipping costs.
Before doing anything with reel to reel, you'd need to read up a lot and get a good understanding of the different types of decks (in relation to tracks), different tape speeds, spool sizes, tape lengths, etc. Also reel to reel decks are usually huge and occupy space. Also operating them is not an easy process like using cassette tapes.
Having said all this, I love tape and cassette decks, and I love vinyl. These interest me, whatever be the case, hence I own these.