Just in case you might like to travel the route of the optimal Sweden tour (and you have available a suitable air/water/land vehicle), we list below the cities in the proper order. We have broken the tour into 100 legs; the link for each leg gives a list of the cities to be covered and a picture of the route to be taken.
Leg 1   Stockholm to Sodertalje | 266 Cities | 507 KM |
Leg 2   Sodertalje to Uppsala | 512 Cities | 1267 KM |
Leg 3   Uppsala to Sigtuna | 41 Cities | 87 KM |
Leg 4   Sigtuna to Hofors | 596 Cities | 1365 KM |
Leg 5   Hofors to Hedemora | 160 Cities | 414 KM |
Leg 6   Hedemora to Sala | 311 Cities | 752 KM |
Leg 7   Sala to Avesta | 107 Cities | 239 KM |
Leg 8   Avesta to Koping | 413 Cities | 983 KM |
Leg 9   Koping to Arboga | 62 Cities | 144 KM |
Leg 10   Arboga to Vasteras | 115 Cities | 246 KM |
Leg 11   Vasteras to Enkoping | 92 Cities | 193 KM |
Leg 12   Enkoping to Orebro | 498 Cities | 1241 KM |
Leg 13   Orebro to Hallefors | 405 Cities | 961 KM |
Leg 14   Hallefors to Ljusnarsberg | 223 Cities | 642 KM |
Leg 15   Ljusnarsberg to Ludvika | 32 Cities | 85 KM |
Leg 16   Ludvika to Gagnef | 118 Cities | 346 KM |
Leg 17   Gagnef to Borlange | 113 Cities | 264 KM |
Leg 18   Borlange to Falun | 146 Cities | 281 KM |
Leg 19   Falun to Ljusdal | 162 Cities | 654 KM |
Leg 20   Ljusdal to Bollnas | 128 Cities | 309 KM |
Leg 21   Bollnas to Ockelbo | 117 Cities | 336 KM |
Leg 22   Ockelbo to Gavle | 119 Cities | 311 KM |
Leg 23   Gavle to Soderhamn | 113 Cities | 310 KM |
Leg 24   Soderhamn to Hudiksvall | 136 Cities | 323 KM |
Leg 25   Hudiksvall to Sundsvall | 208 Cities | 495 KM |
Leg 26   Sundsvall to Solleftea | 1057 Cities | 3605 KM |
Leg 27   Solleftea to Harnosand | 173 Cities | 327 KM |
Leg 28   Harnosand to Dorotea | 226 Cities | 1091 KM |
Leg 29   Dorotea to Vilhelmina | 53 Cities | 239 KM |
Leg 30   Vilhelmina to Ornskoldsvik | 760 Cities | 3335 KM |
Leg 31   Ornskoldsvik to Vannas | 309 Cities | 1038 KM |
Leg 32   Vannas to Umea | 33 Cities | 136 KM |
Leg 33   Umea to Lycksele | 157 Cities | 632 KM |
Leg 34   Lycksele to Skelleftea | 307 Cities | 1382 KM |
Leg 35   Skelleftea to Robertsfors | 262 Cities | 873 KM |
Leg 36   Robertsfors to Pitea | 132 Cities | 432 KM |
Leg 37   Pitea to Lulea | 184 Cities | 872 KM |
Leg 38   Lulea to Kalix | 294 Cities | 1889 KM |
Leg 39   Kalix to Kiruna | 328 Cities | 2099 KM |
Leg 40   Kiruna to Jokkmokk | 39 Cities | 359 KM |
Leg 41   Jokkmokk to Mora | 1575 Cities | 9010 KM |
Leg 42   Mora to Leksand | 117 Cities | 351 KM |
Leg 43   Leksand to Hagfors | 163 Cities | 519 KM |
Leg 44   Hagfors to Eda | 133 Cities | 454 KM |
Leg 45   Eda to Arvika | 68 Cities | 145 KM |
Leg 46   Arvika to Torsby | 134 Cities | 380 KM |
Leg 47   Torsby to Kil | 113 Cities | 254 KM |
Leg 48   Kil to Sunne | 77 Cities | 135 KM |
Leg 49   Sunne to Munkfors | 52 Cities | 105 KM |
Leg 50   Munkfors to Grums | 230 Cities | 544 KM |
Leg 51   Grums to Karlstad | 49 Cities | 112 KM |
Leg 52   Karlstad to Kristinehamn | 139 Cities | 327 KM |
Leg 53   Kristinehamn to Filipstad | 93 Cities | 341 KM |
Leg 54   Filipstad to Karlskoga | 61 Cities | 126 KM |
Leg 55   Karlskoga to Askersund | 178 Cities | 461 KM |
Leg 56   Askersund to Mellerud | 1034 Cities | 2571 KM |
Leg 57   Mellerud to Bengtsfors | 36 Cities | 86 KM |
Leg 58   Bengtsfors to Amal | 54 Cities | 117 KM |
Leg 59   Amal to Saffle | 95 Cities | 174 KM |
Leg 60   Saffle to Arjang | 88 Cities | 249 KM |
Leg 61   Arjang to Fargelanda | 324 Cities | 778 KM |
Leg 62   Fargelanda to Stromstad | 131 Cities | 306 KM |
Leg 63   Stromstad to Grebbestad | 96 Cities | 175 KM |
Leg 64   Grebbestad to Fjallbacka | 15 Cities | 23 KM |
Leg 65   Fjallbacka to Smogen | 53 Cities | 56 KM |
Leg 66   Smogen to Sotenas | 29 Cities | 38 KM |
Leg 67   Sotenas to Lysekil | 66 Cities | 125 KM |
Leg 68   Lysekil to Uddevalla | 335 Cities | 481 KM |
Leg 69   Uddevalla to Kungalv | 283 Cities | 617 KM |
Leg 70   Kungalv to Kungsbacka | 287 Cities | 445 KM |
Leg 71   Kungsbacka to Varberg | 268 Cities | 570 KM |
Leg 72   Varberg to Falkenberg | 53 Cities | 106 KM |
Leg 73   Falkenberg to Halmstad | 54 Cities | 86 KM |
Leg 74   Halmstad to Hoganas | 172 Cities | 366 KM |
Leg 75   Hoganas to Helsingborg | 70 Cities | 123 KM |
Leg 76   Helsingborg to Landskrona | 39 Cities | 71 KM |
Leg 77   Landskrona to Lund | 48 Cities | 112 KM |
Leg 78   Lund to Malmo | 99 Cities | 191 KM |
Leg 79   Malmo to Trelleborg | 54 Cities | 126 KM |
Leg 80   Trelleborg to Skurup | 92 Cities | 221 KM |
Leg 81   Skurup to Astorp | 163 Cities | 412 KM |
Leg 82   Astorp to Angelholm | 44 Cities | 88 KM |
Leg 83   Angelholm to Kristianstad | 593 Cities | 1352 KM |
Leg 84   Kristianstad to Karlshamn | 1038 Cities | 2380 KM |
Leg 85   Karlshamn to Karlskrona | 205 Cities | 417 KM |
Leg 86   Karlskrona to Ronneby | 150 Cities | 283 KM |
Leg 87   Ronneby to Vadstena | 2228 Cities | 5347 KM |
Leg 88   Vadstena to Motala | 25 Cities | 49 KM |
Leg 89   Motala to Boxholm | 108 Cities | 237 KM |
Leg 90   Boxholm to Linkoping | 1457 Cities | 3458 KM |
Leg 91   Linkoping to Atvidaberg | 57 Cities | 137 KM |
Leg 92   Atvidaberg to Finspang | 46 Cities | 130 KM |
Leg 93   Finspang to Soderkoping | 216 Cities | 605 KM |
Leg 94   Soderkoping to Norrkoping | 19 Cities | 37 KM |
Leg 95   Norrkoping to Nykoping | 65 Cities | 183 KM |
Leg 96   Nykoping to Valdemarsvik | 201 Cities | 445 KM |
Leg 97   Valdemarsvik to Morbylanga | 777 Cities | 1759 KM |
Leg 98   Morbylanga to Borgholm | 94 Cities | 184 KM |
Leg 99   Borgholm to Visby | 119 Cities | 309 KM |
Leg 100    Visby back to Stockholm | 909 Cities | 2100 KM |