Chinese hospitals are ranked in a three-tier system (三甲 sānjiǎ being the highest). Unlike in many Western countries, patients often go directly to hospitals instead of general practitioners, which is why Chinese hospitals can be extremely crowded.
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The measure words for 医院 depend on context: 家 (jiā) is most common for counting hospitals as establishments, 所 (suǒ) is used formally, and 座 (zuò) emphasizes the physical building.
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The pattern 医 + place word appears in related vocabulary: 医院 (hospital), 医生 (doctor, literally "medical person"), 医学 (medical science). Learning 医 unlocks a whole family of medical terms.