Hello,
Since I've never been to Spain, I'd love to get feedback on my tentative itinerary.

Day 1: arrive Madrid in a.m.
Day 2: Madrid
Day 3: Day trip to Segovia
Day 4: Train to Cordoba, continue to Seville
Day 5: Seville
Day 6: Seville -- train to Granada in p.m.
Day 7: Granada (alhambra) -- return train to Seville in p.m.
*I know this part seems weird, but we're meeting up with friends
Day 8: Train back to Madrid from Seville
Day 9: Day trip to Toledo, overnight Madrid
Day 10: Fly home out of Madrid

That looks very doable. Just remember to get your Alhambra tickets in advance or get to the Alhambra early in the morning (by 8 a.m.) to make sure you get in that morning.

Do a night tour of the Alhambra. You will not regret it.

It would be nice if you could have another day or two added to your trip, especially in Seville. However, if you can't stretch out your trip I'd say it's both do-able and very good locations.

Busy, but doable. Since your schedule seems set and is pretty tight I would recommend booking train travel in advance (www.renfe.com). While a night tour of the Alhambra would indeed be lovely, according to your plan it looks as if it would fit best in the am on day 7. I would definitely reserve tickets for this in advance (www.alhambratickets.com). The line to purchase same-day tickets can be brutally long (when we went to pick up our 10:30 tickets at 9:00 they were already handing out tickets for 2pm--we were very glad we already had a reservation). And even when booking ahead you still have to wait in the "will call" line to pick up your tickets, which is a lot shorter but can still be a wait. Evenso I would arrive at least 90 minutes before your scheduled entrance time (scheduled time is for entrance to the Palacios Nazaries and they are strict on the time) to allow time to pick up your tickets and see what comes before the Palacios Nazaries (to avoid extra walking in backtracking).

We did a very similar trip recently and loved Spain--hope you do too!

I know this is a busy schedule ... perhaps we should skip the stopover in Cordoba for an extra day in Seville? Thanks to all for the helpful tips on the Alhambra! Depending on our arrival on Day 6, would it make sense to do an evening and daytime Alhambra tour?

Another question: Is it better to take the high-speed train to Seville directly, then visit Cordoba as a day trip from Seville? Or is it better to stop over in Cordoba on the way to Seville?

I have to agree with alan64, more time in Seville would be nice. We spent an entire extra day than what you're planning and didn't want to leave (it was the most enjoyable, relaxing part of our trip). Is it possible for you to add one more day to your trip? Otherwise it comes down to whether or not you're willing to give up some other part of your trip to stretch your time in Seville--ideas might include 1. Skip Cordoba 2. Do either Segovia or Toledo but not both 3. Take the last train back to Madrid on day 8 (hopefully hotel can stash your luggage for the day). You'll just need to figure out what your priorities are. It looks like you're really wanted a good taste of many places in this region of Spain, so you may be fine with the time you have allocated to Seville. If this were my trip, I would be inclined to visit Segovia or Toledo, but not both, just my personal preference. Also I would do the Madrid part (including day-trips) altogether, but I’m guessing you’re splitting this part because of plans with your friends? Your last question: I would definitely see Cordoba as a stop-over versus a day-trip from Seville. Day-tripping from Seville would eat up much more time overall since you’d be adding the roundtrip travel to Cordoba from Seville. It’s really a very simple stopover from Madrid to Seville.

The itinerary looks very doable and should be just fine.

And just for a dissenting opinion? I wouldn't worry about Seville. I was very under-impressed by it. I think it best if you approach this particular city with lesser expectations rather than higher. I was expecting to be blown away by Seville, and in fact, I couldn't wait to leave.

On the other hand, I went to Madrid with very lowered expectations, and found I actually enjoyed the city.

I hope you enjoy your time - Spain is such a lovely country!