Keep an eye open for temporary exhibits, as though they are pricier you can also get discounted fees and the ticket includes a visit to the permanent collection. I saw an Italian baroque exhibition, from artists sorrounding the figure of Caravaggio which was well worth it.
I got the feeling that the guards follow you around with suspicion all the time and felt unconfortable more than once, but it was nothing overtly rude.
I believe you have to go there if in Budapest. Beware of tripadvisor's location, as it didn't appear on my map (offline app) but it is next to the heroes' square.
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