Thank you for your reply.

Yes I mean the island.

Budget wise €70/80 per night if that is possible.

Thank you

I hope this doesn't sound stupid but if you google "hotel ile de nantes" then google will show you a map/results for hotels on the island and adjacent to the island. It appears, per google maps, that there are 4 hotels on the island but there are loads of hotels adjacent to the island that aren't more than a 5 minute walk. Yes, you need to click on the icon for each hotel and check its website for your dates/budget but I'm suggesting this because I imagine it is unlikely that anyone on this forum has stayed at one of the 4 hotels on the island, though I hope I'm wrong and someone will have a specific recommendation for you.

I don't know for which dates or for how many nights as it can make a difference. But i think it will be hard to find something in that price range on the island. You will have to look a little further.

I have found hôtel Saint-Yves at 83 euros per night for a triple room : https://hotel-saintyves.fr/en/ with a bus line that brings you directly to the historic center. Rue Maréchal Joffre closer to rue Sully is a lively stretch with many bars. If you like parks this hotel is also in between the Jardins des Plantes and the Ile de Versailles and its Japonese garden

Otherwise, you will need to look into AirBnBs just make sure they are properly registered with a number starting with "44" so you are sure that they are legal ones.

It's quite a trek from the island to anywhere else really - I'd be tempted to stay somewhere more central and get one of the excellent trams to the bridge on the river crossing which is 5 mins walk from les Machines des Iles. We stayed in the Mercure close to the Place Royal - really handy for bars and restaurants and the Commerce tram stop which went to both les Iles and to the chateau/Jardin des plantes, yet surprisingly tranquil. We got a good deal and paid around the price you are suggesting but you may have to shop around a bit for that. My absolute French city, lots of history but it's passion for slightly bonkers art makes it such as fun place to be.