The southern and northern branches of the Trans-Siberian Railway converge here, so a multitide of trains arrive from Moscow (40 hrs) and the Far East (4-5 days) daily. Aeroflot , OmskAvia , Siberia , VimAvia  fly to Moscow daily (3 hrs). Less frequent flights connect to St. Petersburg (3 hrs), Krasnoyarsk (2 hrs), as well as Frankfurt, Hannover, Köln in Germany (5 hrs).
There is plenty of public transport along the curved main artery prospekt Marksa - ulica Krasnyj Put - prospekt Mira, and to the aiport, bus/ train stations and the river terminal. Trolley N4 & N7, and buses N50, 60 and 69 are particularly useful. The abundant minibus taxis "marshrutka" are an even faster (if at times hair-rasing!) way to get around cheaply. The city center around Lyubinski prospekt is easily walkable and in fact best explored on foot.
Omsk is a convenient hub for several regional attractions. Remember that the distances are large in this part of the world, and a city 700 km away is readily considered "nearby" by the locals. In their defense, the transportation is usually good and can make destinations seem closer than they are.
Tobolsk and Tomsk, the oldest cities of Siberia, are within easy reach. Because the main transportation arteries originally bypassed them, the towns stayed small, avoiding the typical Soviet development, and maintaining their unique character.
For northwestern Tobolsk, take the overnight train, or, better in the summer, take a speed jet boat along the Irtysh River (10-12 hrs). Tobolsk is the picturesque and best-preserved first Siberian capital, with the region's only surviving stone kremlin on the hills overlooking the damp serene flatlands.
Take the overnight train east to Tomsk, Siberia's charming old commercial capital, with its gingerbread wooden houses, hilly terrain and vibrant youthful atmosphere of Siberia's oldest universities.
With time on your hands, consider the weekly tourist-class river cruiser that goes north to Tobolsk and on to Salekhard beyond the Arctic circle (7 days). It stops in several towns on the way, and there is hardly a more upclose way to see the vast sleepy West Siberian terrain, grand rivers and the rural lifestyle. Yet the surreal settlements will surprise you with their quirkiness when you are least expecting it!
Barnaul, the gateway to the Altai mountains and national parks, is 16 hrs by train, and 1.5 hrs by flight. Northern Kazakhstan is accessible by train: Petropavlovsk (4hrs), Astana (12 hrs), or bus: Pavlodar (8 hrs).