I always try to book near the city centre, but when I was planning my trip to Leipzig there were no rooms available at a price I could afford. The Hotel Adler didn't look far away on a map, so, having checked out the hotel's own website, I plumped for it. The directions on the website are slightly wrong in that it is only 7 stops on the tram from the main station, but no matter. It only takes 15 mins and costs €1.80 (about £1.25) for a single journey. You can also buy day tickets, but if you're just exploring the city centre then it's cheaper to buy two singles. The journey from the airport is very simple on the train (about 20 mins). If you buy a ticket from the machine on the platform, make sure it is for Leipzig zone 110. You can then use the ticket for the whole journey (including tram/S-bahn) to the hotel. This will cost €3.40 (about £2.50), and you can do the same for the return journey if you buy a ticket at the main railway station the day before you leave.
There was no problem with check-in. The room (single) was small, but perfectly adequate for my visit and the bathroom was clean with an excellent shower. The TV remote didn't work, but was repaired immediately. The hotel itself is not large (about 20 rooms) and is situated in a very quiet area. There is an S-bahn station next to it (which you can also use to go to the city centre), but I didn't hear many trains at all at night. The breakfast was good (cereals, cheese, cold meats, breads, yoghurt, fruit juices etc) and served until 10am. There is a bar, but due to the small nature of the hotel I usually had to ask at Reception for someone to serve. However, for me this added to the personal touch. The proprietor was charming and nothing was too much trouble. You could take drinks to your room if you wanted.
I don't think this would be a hotel for a family, but if you want to explore Leipzig and are looking for somewhere reasonable, then this could suit you. At €300 (about £215) for five nights, including breakfast, I felt that I had value for money and would certainly consider staying here again.