Having had a quick look around, I think you should visit Sreality. It's the leading property site in the Czech Republic and on my first search, I found a fair number of options in the Pardubice region for 1 bedroom apartments. There are customisable search options (furnished vs unfurnished, location, type etc.) to make browsing a breeze.
If I may ask, what is your budget for rent and transport? The going rate seems to be anything from CZK 5,500 to the more expensive options that go up to CZK 10,000/15,000. The listings are quite informative and also have a feature that allows you to see when they were last updated. I always find that to be useful.
Real Hit also seem to have a good 50 or so listings. So that's quite promising! However, the descriptions are often in Czech. But there is enough english information and pictures for you to make a decisionl, I think. The response email is also in an english template. So it doesn't seem like language would be too much of an issue in communication. Bez Realitky, on the hand, has a decent number of listings but you do have to translate the pages with some often weird results.
For short term lets, have you looked up Airbnb? I think that could come in handy!
In terms of suburbs and localities, the towns of Dašice, Sezemice and Přelouč are all within 20 km of Pardubice. From your basic knowledge, I'm sure you are aware that the city itself is fairly small so public transport or driving a rental car should not prove to be too much of a hassle.
Hope this all works out for you.
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