"Would it be a better choice to stay near Au Haidhausen?"
Generally speaking, it is a good strategy to stay near the main station (Hbf) in most cities, especially if you'll be doing multiple outings by train; outings from the Hbf are typically the most direct, and if you're within easy walking distance, you'll avoid the time and hassle of using a bus or tram both before and after your outing. And usually, the Hbf is the main target for rail connections from a given city's airport, which simplifies your transport on arrival and departure days. Nuremberg's Hbf comes to mind as a really good hotel location if outings are a big part of your stay.
Another general advantage of being near the Hbf is the availability of retail groceries, sundries, etc. on Sundays, when shopping options elswhere are nil.
The Hbf in Munich is a good place to start just about any day outing you have in mind. But it's not the only option in this particular city, and if - like Frankfurt Hbf - it's become a bit sketchy, then the München Ost station may in fact be equally convenient or more convenient for a given outing, depending on the outings you plan to take, and perhaps your Au Haidhausen hotel options put you close enough for a quick and easy escape from Munich. München Ost also offers direct rail access to/from MUC Airport. Just don't expect Sundays (or any other day) at the München Ost station to be full of shopping options, eateries, etc.