It all depends on how much money Israel continues to receive. If they can get someone, anyone, to pay the bills for their military, they can continue to hold on to the land for as long as they want. If they can't pay for their army, they'll need to draw down their forces, and a face-saving (for all sides) peace treaty is the best way to do that.
Holding the east bank of the Suez is no harder - and in fact, probably easier - than the current Israel/Egypt border.
I see Israel withdrawing to the Suez and holding the territory indefinitely and annexing it. The population in 1960 (the most recent census before 1967) is 45,000, and IIRC much of the non-Bedouin population fled after Israel's capture of the region*. IOTL, Israel actually began a fairly aggressive plan of settling the peninsula, which will no doubt continue here. Within a generation, I see the Sinai being considered as integral a part of Israel as the Negev. The oil will be developed and go to Israel (solely), and the tourist industry will develop much as IOTL.
I'm not sure if Israel will be able to hold the Suez canal - as of the ceasefire, they didn't hold Port Said. They'll probably withdraw to the east bank and consolidate. That's not gonna be good for world commerce - I expect the Suez to be closed for a while, though - probably at least a generation. At least Russian petrochemicals get a boost
No treaty with Egypt definitely handwaves the treaty with Jordan (the long running joke in Israel was that Jordan would be the second Arab nation to sign a treaty with Israel). Honestly, I have no idea what that does to the West Bank (which Jordan formally waived their right to in '94). The Jordanian economy is going to see a little bit of a hit relative to OTL from lost trade and tourism with Israel - but such a small hit it probably won't be noticeable.
Now, the West Bank and Gaza. This is going to be fun! Gaza's population in 1967 is 280,000; Israel's is 3.5 million (~2.5 million Jews, 1 million Arabs). With Gaza being entirely surrounded by Israel, I see Gaza getting an East-Jerusalem style annexation. By which I mean, most Gazans will be offered and reject citizenship, instead receiving permanent residence and holding out for the hope of liberation in a Palestinian state, while Israel chuckles, knowing they'll never give up the territory. Some terrorism will continue, but with Israel controlling all borders, it'll be hard.
It's possible but IMO unlikely that Israel will also annex the West Bank; honestly, I think the most likely thing is OTL's situation for most of that time. Jordan's probably still going to cede their claim to the region in the late 80s, though I suppose it's possible they'll keep claiming it. How the lack of Gaza is going to affect the Palestinian liberation movement...I have no idea. It might even make things better (historically, the PA's had some trouble relating to their responsibility over two non-adjacent pieces of land). The situation in Gaza is almost certainly improved, though, more like Israeli Arab standard than the current hell-hole it is now.
*Fled, was expelled, whatever; I don't want to get bogged down in that conversation as it's not particularly germane to the discussion