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Logistics is Key
For a trip of 2-3 days, choose cities with an airport not far from the center (or with a fast metro/train). Spending 4 hours on transfer in a short trip is an impermissible luxury.
Fly only with carry-on luggage. No waiting for baggage.
Accommodation in Center
It is better to overpay for a hotel in the center than to spend time and money on transport from the outskirts. In a short trip, time is the most valuable resource.
Minimum Plan
Don't try to see everything. Choose 1-2 main museums or sights, and spend the rest of the time just walking, soaking up the atmosphere, and eating delicious food. Racing through a checklist will only tire you out.