Lac du Lauzon, my favourite hike, saved for last. This is an hour long drive from Gap but definitely my favourite. You can park your car at Chalet-Hôtel du Gioberney, La Chapelle-en-Valgaudémar after which ,the route is pretty easy to follow up to the lake. It takes about 2 hours to reach the lake and another hour to come back down. Depending on how hot it is, you can take a refreshing dip in the lake or under the waterfall to cool down.
In any case, if you are not used to hiking, I wouldn't recommend going alone or going with people equally clueless as you, unless there are lots of people you can follow or you are 100% sure you know what you're doing. It is also very important to check the weather forecast because you don't want to get caught in a situation you can't get out of. The most important tip would be, knowing when to say no and not doing stupid things in the mountains that can put your life in danger. If you're unsure, you could always hire a guide.
If you land in Paris, you can take an overnight train that reaches Gap early in the morning and can be as cheap as 30 euros. If you land in Marseille, there are many trains to Gap for 20 euros and it takes about 4 hours or blabla cars (an intercity carpool service application that is very trustworthy) as well. As for the stay in Gap, there are numerous beautiful airbnbs that cost about 20 euros per night in the centre of the city from where the restaurants, bars, supermarkets, station and bus stop are accessible on foot. I suggest visiting this region during the months of April-May for Spring or September and October for Autumn. During June and Juy, it gets way too crowded and the temperature reaches more than 30 degrees. Whereas Spring and Autumn are hot enough to hike during the day and cool enough to enjoy the cool breeze by night.
Must try foods in this region include Tourtons (they are like fried pockets, they can be sweet and savoury) , Oreilles d'ânes ( which literally translated means Donkey's ears but, it's just wild spinach gratin and crepes/lasagna. It is named so because cooked Spinach resembles floppy donkey's ears) and Raviolis (The Champsaur ravioli is a kind of quenelle, made from potatoes and eggs). The best restaurant for all the cheese-lovers to try a raclette and fondue is "Le refuge" in Gap, where you should try the after meal digestive liqueur called "Génépi" which is made from flowers in the region ( Keep in mind that it is really strong). If you're craving Asian food, I'd suggest "Saveur d'Asie", for burgers "Chez Fred" and for some good old pizza "Giuseppe". For drinks, my favourite go to bar is "Au Ch'ti Bar" which is famous in Gap for its Belgian Beers. "Bistrot Gapençais" and "The Black Lions" are also great bars. If you're looking for something slightly upscale or fancy I'd recommend Le Beau Soleil. All of these are in the city centre and you can just walk from one to the other. If you're feeling like dancing one night, believe it or not, this small city has a nightclub about a kilometre and half from the city centre. It's a 25 minute walk but guess what? You don't have to walk all that way. Instead, you can call them up and request a shuttle to come pick you up and drop you back home at the end of the night. Isn't that just so nice?