Well, first of all congratulations – you have made a pretty good choice for a tourist destination. Spain is definitely a great country, especially when it comes to do some sightseeing and meet interesting people. It is good that you are making a research on internet on what should you do because it is a huge country. Of course it is better to know where to go. My opinion is simple. If you have around 10 days I would recommend you to divide your stay in Spain in different cities. In that way you will be able to see most of the things worth seeing plus you won’t get bored. Here is my personal ranking. Of course it depends on your entry point but here is at it goes. Day 1 to day 3 you should stay in Madrid. Day 4 to day 5 - Seville. Day 6 in Grenada and day 7 to day 9 in Barcelona. Basically these are the 4 cities you must see while you are in Spain. Each one of them is beautiful and has lots to offer to a tourist. Now the next thing you should have in mind is the means of transport you are going to use. Of course as you know the easiest and most comfortable way is by car but if your budget is not enough sufficient you might want to take the public transport. Don’t worry, the infrastructure is well developed in Spain and this is why you will not have any problems with catching a bus or a train. Unfortunately I can’t give you exact prices or schedules of the public transport because I’ve never been to Spain but I’m sure that the internet stores lots of useful information on this topic.
Some people will tell you that my offer to visit all of the four above mentioned cities may sound a bit rushed but it is up to you. I’m sure that if you are on vacation in Spain you will have lots of free time and therefore you will visit many interesting sights in the cities. Two days are more than enough for a tourist in my opinion. Anyway, it is your right to disagree with me.
The last thing I’m going to tell you is the accommodation. If you are going to stay for day or two in a certain city why don’t you consider the idea of renting apartment? Apartment Barcelona and apartments in Madrid can be found pretty easily plus I don’t think that you will want something pretty luxurious since you are going to stay there for such a short period. It is easy to find accommodation there. For example if you want to find Apartments in Milan or Vienna apartment for rent it will cost you more time and efforts. This is why my personal opinion is to take advantage of the fact that the prices of accommodation are low and have one great vacation in Spain!