1

bed bugs are a fairly rare commodity in Europe compared to the US and i personally have not heard of any major bedbug outbreaks in Prague and I have stayed in numerous hotesl, and apartments in the city.
You might consider a studio apartment to stay in, lots available and it usually works out cheaper than a hotel, ok you may have to arrange your own breakfast but thats no major worry.
http://www.travelcook.com/
this company are well regarded and I have booked with them in the past and am staying in one of thier properties in october. this is where I am staying
http://www.travelcook.com/229-apartment-residence-husova-prague
it is fairly central and well within your budget.
I stayed recently in the Hotel DAP
http://www.daphotel.cz/index.php?/english/
and that was very good, right on the roundabout at Dejvicka just 40 yards from a tram stop and about 60 from the metro entrance, will get you to anywhere in the city with 20 minutes easily.
http://www.okhotels.cz/en/hotel-orion
this is another place i stayed in about a year or so ago, small apartment style hotel, not luxury but pretty good had a small attic apartment to myself and they provided a great beakfast, about a 5 minute walk from Namesti Miru Metro/tram interchange.
there are lots of cheaper places in the Zizkov, Vinohrady,Smichov ,Dejvicka and Karlin areas, not city center but close enough to be walkable or a short tram or metro ride away.
personally I love the Dejvicka area but mainly for its great transport links but more because some of my favourite pubs are there .
hope this helps and at least gives you some ideas

2

I´d rather not stay at Legerova as it´s a major transport vein of Prague, and the traffic and noise can get really obnoxious there.
As for bedbugs... you´re more likely to get them in Paris than in Prague, imho.