Without vials and assuming you have Patron, Trion's version of doing subscriptions, your best bet is probably doing IA's until 50.
50-59 would be doing the zone quest lines in Storm Legion. The Dusken or Brevane continents will be activated when you pick up the quest in the mail - either or will provide good exp.
59-65 (preferably with 160% exp vials here as the levels will drag if you can afford them) would be in the Nightmare Tide expansion going from zone to zone following the quest line. Here and there you can do carnage quests because in the area where the quests takes you, you'll have them around. If you're limited on time and/or can only play once in awhile, remember that once you finish a major area (it'll provide an achievement) there are daily quests activated that will give you around 300k-400k base exp. A good tip for easy exp with dailies is that when you get to the Ghar Stations (Mem, Rosh and Tau), the Manugo daily quests are simple and only takes about 3-5 minutes to finish. You can pick all 3 up (I believe there's a level requirement for certain areas) and do them all at once.