About Luxembourg
Luxembourg is quite historical city and many may find it quite small but it makes traveling much easier honestly.
What I Have Done Before Going
Generally, before going any city or the country I do a quick research on google and start to get familiar with the places. However, if you do not want to search on your own, there might be many tours to there as well. So, check both options out because sometimes one of them could be quite cheap. When I plan to stay in a place for a night, it is always much better to book hostel in advance because cheaper options are mostly sold out when the days are getting closer. For Luxembourg, my personal advice would be if you can arrive the city early in the morning then one day is enough but you may fell in love with the city and want to stay one more day. For budgeting, one day is enough. In case you want to stay for a couple of days, then check out either booking.com or hostels sites.
Staying in Luxembourg
I stayed at Youth Hostel. Compare to other places in the city it may seems far but it was just 15-20 min away to city center by walking. Additionally, it is so close to river. So, you will have a nice atmosphere on the way to city centre
What to eat?
I searched for Vegan places but I also saw so many good restaurants and they are all in one place. Let me tell you about Vegan places, maybe you will like it. There are not bad :)
Beet
It is known as a vegeterian restaurant. At least, I thought so. However, after my Vegan Burger I was quite sure that the place is Vegan restaurant. I can't tell that it is cheap but if you are starving you can eat one meal for your two meals in a day such as instead of eating at 12 pm, you can eat at 3-4 pm and there won't need for dinner. Believe me. The price I paid was €15 Euros for burger, patato and salad. It was pretty much for me and I skipped the dinner.
Flowers Kitchen
If you hungry right after you arrive, this place can be life saver because it is close to train station and cozy place to eat something. I drank Matcha Latte. So, unfortunately I can't tekl much about the taste of the food but the people over there were quite nice.
Cathy Goedert
This was my favorite place honestly. I do not know whether you like sweet things but if you do, this is the place to try new things. Their products are qualitive and delicious. I asked for the bestseller but they told me there is nothing left at the end of the day. So, all of the pastries are the bestsellers basically.
Coffee Fellows
I like this coffee because they have Matcha! Sometimes it is quite to fond matcha in Europe. So, if you miss how Matcha tastes like, this is the place to go! Additionally, they have sandwich for everyone! This place is originally German, München. So, you can try out in Germany as well.
Downtown Cafe
I could not have chance to try but this place seems cool as well.
Amorino
If you like try something new or ice cream, this is the place to go. Maybe from other European countries you have heard this place. They are quite known. Unfortunately, I could not find in Germany but France.
What is different about Amorino? When you order your ice cream, you basically choose any of the three sizes. Then you can add any flavor as much as you want. Additionally, you can add Macaron in the middle if you like. I just loved this place!
Urban Bar&Restaurant
I saw this palce but I could not have chance to get in. However, if you are looking a place to eat dinner or having a great talk while you are resting, this is great place to chill!
Chocolate House
The whole time I looked for something special for Luxembourg and I finally found dessert in this cafe. However, I did not taste it because it was not Vegan. However, if you are not! I really recommend you try. Moreover, they have any kimd of chocolate that you can make your own hot chocolate. The only thing you need to do is to chıose the chocolate type you want and which milk you want. They you basically take you chocolate and dipp into milk until it is melt. If you do not want to drink right away, you can buy it and try at home. It is perfectly fine and delicious!
I think this is all I know about place to eat or chill.
Let's get to the real part!
Historical and nice places are quite close to each other and you can get around pretty easy. So, take a deep breath and dive into this historical land.
Adolphe Bridge
This bridge has great view but from my point of view, seeing both the bridge and Plateau Bourbon is perfect!
Plateau Bourbon
The view is enough. I should not say a word! It was love at first sight for me. This picture is quite far away but it becomes way much better when you see from the opposite direction which there is a huge gap between you and the Plateau.

Bei de Bouwen
You can see this view while you are in escalator on the way up to the bridge level. It is quite impressive because the neighbourhood at the bottom is quite nice and chill. Then, you are going all the way up free and you are so close to the museum and Theme Park. Honestly, I was a little bit sad after I went down because it means that I have to go all the way up which means an hour for me to go to museum. When I found this way to go up and when I learned that it is free, it blowed my mind! I just loved the city more. and it is quite interesting to pass the bridge by walking on the way to Museum.

MUDAM Luxembourg (Museum)
I got into the museum free because I am student in University of Mannheim and since you will be the student as well, it is quite easy to get in this beautiful museum free. There are so many great contemporary art pieces from different artists. Honestly, I was not expecting that because it was -according to Luxembourg scale- quite far from the city but it was AMAZING! If you are not really into contemporary art, there is also another amazing view of the city right behind the museum.
Fort Thüngen
As I told you there is a view point, right behind the museum which is quite interesting and beautiful because it is quite hard to find if you do no search for it. Isn't that amazing?

Schlassbléck
If you want to take the most of it from the view, I highly recommend you to visit this view point early in the morning like 7-8 am. Or sometime before 9 am. Because even though there are not much tourist on the view point, it is much better to see the view without any distraction. If you are lucky enough, you can see the view without any fog.

This is not the perfect picture from the point. However, I was more focused on watching the view than taking pictures of it. My bad!
Palais Grand-Ducal
Honestly, it is not the best place to see but the palace seems quite nice. If you have chance to drink something in Chocolate House, this palace will be a great view for you to watch.

Cathédrale Notre-Dame
This is the church of the city I guess. However, after so many churches I guess I lost my interest to them. So, I do not know what is inside of the church. Let me know if you get in.

Monument of Remembrance
This is a great monument and the view behind is amazing because this is the place I mentioned why I was talking about Plateau Bourbon. Check this place out because the view is breathtaking.
At least, was for me!
There are couple of more places to see but I am sure you will see all of them while you are wondering around. Do not forget to walk next to the river it is the most peaceful part of the trip!