That is a 3.2 km, or 2.0 mile walk. 40 minutes for your regular type person, maybe 35 for an athlete. Add another 15 minutes to reach the farthest historic sites.

None of the hotels you listed is very close to the arena at all, depending on your definition of "close";

Am Blumenhaus is 2.5 kms from the arena - the best position to split the difference between the arena and touring
Hotel Café Bergschlösschen is way on the other side of town - 4.7 km away
Hotel Andres is 3.1 km away
Hotel National is 3.0 km away

I really don't know of anything close to the arena - maybe someone else does......

If you map this trip on google, it give a distance of 5.5 kms by car. It doesn't even give an option for searching for pedestrian directions, so Im assuming a good 6 kms or so, maybe an hour along city streets to walk to the Altstadt.
Better to investigate whether there is a bus connection between the two!

http://maps.google.com/maps?ll=49.897122,10.880499&spn=0.02488,0.04549&z=14&key=ABQIAAAAGS-o77vq2-GaFOdhfNrGchS9lY-ThE3B0DnmEH5tCbt9es42ahTtZPAg5V_ru8VmdjRnaSQ_a5h3lQ&mapclient=jsapi&oi=map_misc&ct=api_logo

Thanks guys! It looks like I misjudged something when I was looking at the map. So, what would you suggest me to do? Should I stay in hotel close to historic sites and then use buses to reach Arena if there is good connection?

That would certainly be MY preference, especially if you are only spending PART of each day at the arena. Then you could explore the wonderful town itself each ?evening, or whatever part of each day is free.
If interested in my Trip Report to Bamberg this May 2012, click on my name and scroll down.
Don't miss the wonderful brewery gardens and the local dark, smoke beer (Rauchbier).
Otherwise, a bit more searching finds these options:
1) Hotel Garni Alt Wunderburg at Kapellenstrasse 26, approximately 2.6-3 kms by auto from the area OR
2) City Wohnung Sonnenschein at Nuernburgerstrasse 161 at 1.0-2.3 kms from the arena (if you must- the only thing is that the area by the arena is reached by major highway)!

Eureka!
It looks like bus lines 935 and 920 lead from th ZOB (main bus depot in town) to the Stadion (or arena).
From the ZOB stop it is but 10-15 minutes to the main attractions of the Altstadt.

http://www.verkehrsbetriebe.de/cms/OePNV/Liniennetzplan/Liniennetzplan.html

Thanks a lot mokka! I will read your Trip report too...