Egypt is certainly near (about 5 hours flight, I think) and cheap, but unless you want to spend all your time in the sea (which will be rather cold in January) or around the pool, there is not much to do. I have stayed in Marsa Alam, Hurghada, Sharm (twice) and Nueweiba (twice) and I have made forays out of the hotels either on boat trips or by taxi to the nearest town, or once on a 'jeep safari'. I found the towns very dirty and ramshackle and the snorkeling from the boat trips was in large groups, which I hate. Traders stand in your path outside the shops and whilst they are not threatening it can be annoying You can, of course, fly to Luxor or Cairo, at some expense, or even Petra, but that rather negates the plan to find an inexpensive holiday. I think the FO is still advising against visiting the big towns in the North of Egypt. No problems in Red Sea Resorts.
I would go to Egypt only for snorkeling on the wonderful coral, and I would not go in Winter.
Of course, the best hotels will offer a programme of activities but I fear none of them would appeal to me.
I spent one disappointing holiday in the Maldives, because the coral was bleached and there was absolutely nowhere to go as the entire island could be cirumnavigated in 20 minutes. I like to be active on holiday - I can lie around as much as I like at home. I enjoy visiting historic towns/ villages and seeing beautiful scenery - not much of either in Egypt.
Tour operators are desperate at the moment, so if I wanted to go away I would look for a package to one of the bigger Caribbean islands - Martinique or Guadelope , or Cuba.