The nearest bigger railway stations to Königswinter are in Bonn, Cologne and Siegburg, but Königswinter also has its own railway station. It can by reached from Cologne by a regional train going to Koblenz. But make sure that your train is travelling on the right side of the Rhine, not via Bonn on the left, and that your train stops in Königswinter.
From these stations you have to travel by Regionalbahn, Regional-Express or tram (Stadtbahn). Long distance trains might pass Königswinter withot stopping. From Siegburg or Bonn you take the tram 66. Be careful that you do not use the train that is just going up to Ramersdorf.
You need a train going to Königswinter or Bad Honnef. From Cologne you can either take a Regional-Express or S-Bahn to Siegburg or Bonn or get Tram (Stadtbahn) that is directly going to Königswinter. Mostly, these are trains from Cologne to Koblenz but only those on the Rhine's right side. You must look for trains passing Deutz, (the airport of Cologne), Troisdorf and Bonn-Beuel. Trains travelling to Koblenz via Bonn and Remagen won't bring you here.
By boat, you can reach Königswinter with the tourist boats on the Rhine and by ferry from Bonn Mehlem, but this is not useful only if you live in Bonn.
You can reach Königswinter directly from one of the biggest German motorway, the A3. Just take the exit "Siebengebirge" and follow the signs over the "Margarethenhöhe". If you are coming from Cologne, you might also use the A 59 to Bonn and Neuwied. This motorway is also the way for you if you are coming from Bonn.
Just cross the Rhine and enter the motorway. Then, you will have to take the exit "Königswinter". After you enter the town, signs lead you to parking places.
Königswinter consists on the one hand of the "main city" directly in the rhine valley and the suburb of "Dollendorf" and on the other hand of many many bigger and smaller villages in the Siebengebirge, such as Ittenbach, Oberpleis, Stieldorf, Heisterbach or Thomasberg to mention the main one's.
Next to visiting the City of Königswinter you might go walking in the "Siebengebirge". In here you'll find much more (and sometimes even nicer) places, than the Drachenfels. A good point to start going through the forests is the "Margarethenhöhe". This can be reached by the bus 520 from Königswinter or by car. You'll find parking places here, but you have to pay for then and - espacially in the summer and on weekends - have to search them. From here you can go to the Ölberg, the region's highest mountain, with a nice view on the landscape. (about half an hour) You can also walk to the Löwenburg, an old castle from the middle ages - or what you can still see of it, as it's a ruin. (about 1 to 1 and a half hour) Or you can go to the Milchhäuschen, a small restaurant in the forest (about an hour) and further to the Drachenfels (another hour). If you take the bus 521 you can visit Oberdollendorf with small old houses and wine restaurants and you can go to Heisterbach, a ruin of a church inside the forest.
Essentially all of the shops are located just east of the Rhine River, on the town's main street. Since there isn't a wide variety of shops, most shops are geared toward locals, however, since Königswinter is a noteworthy town in the Siebengebirge region postcards and other souvenirs are available for purchase.
You will find small fast food stores which offers french fries, saussages, etc. as well as very good restaurants in here. Most of them can be found in the main street, at the rhine and on the way to the Drachenfels.