Last year my parents stayed in the Kaleici, the old quarters of Antalya, at MOND HOTEL PENSION and were very happy there.
The pension has 25 rooms, the best one being the KING SUITE, with its own balcony under the roof, with a view of the marina, boats, sea and little side streets.

It was very reasonably priced, and although the rooms are basic, they are clean and the owner went out of his way to help my parents during their 2-week stay. Nothing was too much much trouble for him and he was a very kind-hearted and genuine person.

For further information pse go into www(dot)mondpansiyon(dot)com

How about Suite Laguna Hotel and Argos Hotel? Both are lovely, both are located close to the historic district and both are inexpensive (40-50$ for a double room). Each of them has its specific advantages. I do recommend both. If you wish to see how they look like, you could see their photos on easy click travel web site. That's where I booked them. These are my recommended accommodations nearby the old quarter of Antalya

As you say on your post, I still did my own research about the hotel. I have found out that the Mond Hotel Pension offers tastefully and carefully furnished rooms, in order to meet all your needs, and modern communication technology. In the morning guests are pampered with a delicious and rich breakfast.