Perfect location for the stadium, it will be stunning.
I recommend you stay at the Marriott, you can have a beautiful walk to the stadium from there. If you want something closer and cheaper, stay at the Hotel Thomas. It's pretty cheap but fully adequate for low budget crash pad. The Marriott is pretty nice; not sure how expensive now (we used to get a great deal there 25 years ago) but the location is great. If you want something even more modern there is a Kempinski near the Marriott but it's not on the river.
I haven't been to Budapest since 2004 so there might be even better options, but I'm sticking with my recommendations for the Marriott or the Hotel Thomas depending on budget.