Ok, you have a weekend in the absolute highest tourist season in one of the most popular destinations in Japan (and five days). Your choices are severely limited - so either stay in Nagoya and take the 40 minute train, or pay the going rate. A quick search:
MyStays Shijo: I use this hotel quite often. Reasonable location and comfort level. A bit business hotel, and I don't eat in the hotel. I have six rooms booked there the following weekend because I couldn't get extra at my first choice location (the Century) which I booked months ago.
Tokyu Hotel: I think it is a slightly unusual location, but there is a shuttle to the station and I use this chain in other cities, so should be ok
Hotel Brighton: I see others recommending this hotel, but I do not have personal experience of this one.
The other hotel that came up was the Mitsui Garden. I used one of their properties in Sendai and it was ok, but I had feedback about the property in Tokyo (Ueno) that it wasn't really good enough (I had done a booking for someone as a favour), so I can't recommend that.