The Seychelles consist of about 115 islands but you are not able to reach all of them easily. The main islands are Mahé, Praslin and La Digue which belong to the so-called Inner Islands. Thus, if you have only about 3 weeks for travelling, you should focus on these islands. Travelling the Seychelles on low budget is definitely hard. Although airbnb places seem rather expensive, it is the cheapest way to sleep. Make sure to book early in advance because there are not many offerings.
Tip: You can also contact hosts and ask for permission to set up your tent in their backyard to save some money.
The main islands have an appropriate infrastructure. You can take buses on Mahé and Praslin to get around. When visiting La Digue, only bikes are allowed. Keep in mind that the ferries only operate one to three times per day. If you need a speedboat, it is advisable to book them directly at the beach after nicely talking to some private providers.
• La Digue: First of all, visit Anse Source d'Argent. It is one of the most beautiful beaches I have ever been to. But make sure to be early (before 10am), otherwise it'll be crowded due to its famous rock formations. Secondly, rent a bike and ride around the island, it is just beautiful!
• Praslin: Visit Anse de Georgette. Start at Anse Lazio and hike via Mount Plaisir to Anse de Georgette. It is a really beautiful hike and the beach is totally worth it. Watch out: Local people are waiting at Anse Lazio to show you the path across the mountain to the beach - of course not for free! Use your smartphone, e.g. maps.me, if you want to save money. Additionally, you should spend some time at charming Cote D'or Beach/Anse Volbert. Some small restaurants are around and there are just a few waves.
• Curieuse Island: This is the absolute best spot. Make a half day trip to this island and walk around huge turtles, beautiful rock formations and through beautiful landscapes. You will have enough time to take pictures with the turtles. Make sure not to pay more than 50€ with local guides.
• Mahé: Usually you'll have to spend at least a day here because the airport is located on this island. Mahé has nice beaches and at least a little nightlife but this island is no must-do. Anyways, the Mirante la Misere is worth to be visited. It gives you a nice view of the other islands and Mahé itself. Make sure to sleep at Christabel's place.