If challenged as to how many places to see in an evening in Budapest, then follow the below path and I am sure most of the things will be covered in one evening

Let’s say, one is starting from Gozdsu Udvar Court on a weekend, then this is what one can see as a tourist and where one can eat. 
Then you can literally walk towards your next stop after a short 15 minutes walk. 

St. Stephens Basilica Church

As you walk away after admiring the iconic St, Stephens Basilica from the inside, look back at the basilica, you have a photo opportunity, you shouldn’t miss. It is the shot you would see in next image

As you start walking away from the Basilica, you will pass the Fat policeman Statue. Say hello to him,  offer him to eat an ice cream from the nearby vendor and start walking straights towards your 3rd Spot of the evening.

Szechenyi Chain Bridge
This iconic suspension bridge serves to connect the east and the west of the capital of Hungary, Budapest. It connects the Buda and the Pest region on the two sides of the Danube river. Once you reach the bridge, you will realise that the vibe surrounding the bridge is of relaxation even though the bridge is constantly crowded with traffic. One can walk on the bridge. It is a 10-15 min walk if you do not wait to admire the flowing waters of the Danube river. Actually, my recommendation is to look around while walking from the right side of the bridge when coming from the Basilica. Below pictures will give an idea of what to expect, I am sure you won’t want to miss these views. 
 

As you reach the other side of the Bridge, I would suggest walking towards the Rudas Baths. 
What many people are unaware of Hungary is that they are famous for thermal water baths. Large public water baths are located in different parts of the city. I would say it is a must experience when in Budapest. Visit one public bath for sure. I have no pictures from this place. I would like to highly recommend this place because they also have an open hot water bath on their roof, which looks over the entire Budapest city. 
It was dark and almost near their closing time when we reached this bath, but that was even perfect. We had the most mesmerizing view of Szechenyi Chain bridge from this spot. I didn’t have a camera for obvious reasons but that view is etched in my memory. 

As we walked towards our Hostel, we again crossed the bridge and got a night view of the city. We had a late dinner at Cucina Italian Kitchen with our heart’s content after spending an absolute productive evening in Budapest.