Hey, Welcome to the boards!
Does this $3,000 CAN budget include your plane ticket to Europe or travel between countries?
That roughly 2,000 euros for 19 days, or over 100 euros a day. You can easily stay within your budget as the summer travel season won't be kicking in to high gear until July, and that's when the rates will increase.
hitting your accommodations budget each day along with about 10-20 euros for food each day, you'll still have about 40-50 plus euros left over each day that will carry over into the budget for the remaining days, giving you a lot more lee-way to splurge. So by the second week, your 100 euro a day budget will go to 150 euro budget per day. That's a great position to be in.
Are you going to be traveling by Eurail, buses, or cheap flights?
And yes, your itinerary looks just right if you don't care about settling down for an extended length of time in one city to do some deeper exploration, meet some locals, and really get to know a city. If you do want to do this, I would shave off one city on your list and give those days to the city you want to explore most. Or, keep the same itinerary and shave a day off 2-3 cities and add those to the main city on your list. Hope that sense.
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