2 weeks in South Africa and 1 week in the Seychelles

Seychelles is not an island, but many. A little bit over 100 islands, but the main three are: Mahe, Praslin and La Digue.You need to stay at Mahe or Praslin, but spending one day visiting La Digue is worth. La Digue has one of the top beaches of the planet, called Anse Source d'Argent (Silver Fountain Beach).
I personally prefer Praslin, with the beach Anse Lazio as one of the most beautiful of the island, because it also has a forest that is declared human patromony from UNESCO, several other things to do and is more relaxed than Mahe.
The capital, Victoria (Seychelles), is located in Mahe. There's a very nice area with many hotels called Beau Vallon to the north of the island. There are some atolon islands in Seychelles but the main three islands are rock solid, so although snorkling and/or diving is a must, I'd say it's not at the level of Maldives. There are not so many coral reefs as in other paradise islands and several of the beaches are quite dangerous with strong currents. The ones I have mentioned so far are safe.
The prices are usually high for hotels and flights. It's managed as an exclusive destination, but restaurants outside of the hotels have a reasonable price and so the taxis.
I spent three days in Praslin and four in Mahe when I was there.
I hope my information is not too outdated because I was there some years ago.
Indeed one of the top destinations of the world and in my view worth every penny.

Hi Lise, we visited Cape Town a few years ago and stayed at the Cape Cadogan a small boutique hotel, really cannot recommend it enough, lovely rooms, friendly, helpful staff. Area was very safe so we could walk everywhere in town, and also very close to some excellent restuarants (which was a priority for us!). Possible things have changed with covid but you would likely need to book restaurants ahead of time as they can get booked up, the hotel was very good in doing this before we arrived and managed to get us into some places we would not otherwise have been able to book. We were there in early March and the weather was perfect so anytime between mid Jan and early April should mean warm, sunny days. We love our wine too and made several trips out to the vineyards, Stellenbosch has some amazing places to visit even if you're not into wine there are great places to walk and have lunch. Hope this is of help and wishing you a fantastic trip and hope you enjoy your big birthday!

Hi Lise,
Greetings from Cape Town!
Your trip idea is on the right track - two weeks in South Africa and one week Island is perfect. 
I'll recommend using a local agent here in South Africa. The more "middle men" you cut out the more you'll save and the more goes directly to the properties and suppliers in South Africa.
If you use an agent in the US, they will just call an agent here and book it for you, taking a % of course. But it's up to you and what makes you comfortable.
I can recommend TravelHouse Africa, they are based in Cape Town and have assisted many friends and contacts. They are also in tune with clients needs and won't recommend something that doesn't suit the client (this happens often when using a agent that isn't based in the destination). 
let me know is you need more information.
regards,
Dirk