If you're playing Birthright then there will often be other maps usually labeled "Challenge" when you leave the castle. You can fight the enemies on those maps to get extra EXP and gold. You can also select "Scout" on the list and pay some gold (which in Birthright you will likely be drowning in) to spawn a new group of enemies for you to fight on any map you've previously cleared, of your choosing. You can do this as often as you have gold to spend.
EDIT: I have finally played through both Conquest and Birthright and have finished my Lunatic Awakening run, so I plan to start Revelations very soon. And I have a couple of questions before I start down that path:
1) Is Hidden Truths something to do before or after completing Revelations (or is there even a point partway through where it's alright)?
2) I have heard some of you say that the unit balance in Revelations is pretty bad. Besides Corrin, Jakob, and Azura, who is worth using? Who should I not bother using?
1) You could do Hidden Truths 1 before completing Revelation since it doesn't spoil anything major, but Hidden Truths 2 should definitely be played after beating Revelation since it spoils some big moments from that route and is mainly there to answer some unresolved questions from Revelation.
Both Hidden Truths maps will give you rewards if you complete them without losing a single unit. The first one will award you with a Fell Brand, which allows a male unit to reclass into the Grandmaster class. The second will award you with First Blood, an item that allows a non-royal unit to activate Dragon Veins.
Personally, I recommend saving Hidden Truths until you beat Revelation since both maps are far more enjoyable if you play both of them in one go. First Blood probably won't be very useful though regardless of when you complete it since you have access to 10 royals in Revelation. If you want to give a unit some Grandmaster skills, you could complete Hidden Truths 1 before beating the story, but I didn't really need to use the Grandmaster class or its skills in my playthrough of the route.
2) All of the royals are worth using. As for the others, most of the Hoshido units are not affected by the horrible unit balance. The only ones that get the short end of the stick are Rinkah and apparently Hana and Subaki. Personally, I found Rinkah, Hana, and Subaki pretty useful from the get go. You get Hana and Subaki after completing Chapter 8, and what I did was tackle Mozu's Paralogue after completing that chapter to give them a good opportunity to catch up to speed for the next chapter. Rinkah makes a really good pair-up bot in the chapter she is introduced because of her Strength bonus, and if you ever need to land a kill, you could switch into her to do so and gain some EXP for her. Chapter 9 is also the perfect map for any lower-level units to grind up since you're only allowed to use six units for that map. Only problem with that chapter is that it has one of the worst maps in all of Fates because of its tediously boring map gimmick.
Orochi also is a bit on the lackluster side in the chapter she is introduced, mainly due to the fact she first appears in Chapter 11 where there are lots of ninja units. If you want to recruit her, you need to kill the enemy ninja located above Saizo right away or else that ninja will head straight for Orochi and easily kill her. Once that ninja is defeated, talk to Saizo, and he, Orochi, and Reina will be playable afterward. Following Chapter 11, Orochi does pretty well in the following chapters.
Much of the unit imbalancing can be seen with a good chunk of the non-royal Nohr units. The only ones that were pretty good from the chapter they were first introduced were Selena, Beruka, Silas, Benny, Keaton, Laslow, and Peri. Silas is particularly noteworthy since he joins you after beating Chapter 14 and arrives at a pretty good level with B Rank in both swords and lances already. As for Benny, he is the only Chapter 14 recruitable unit, bar Silas, that arrives at a level that is around the same range your units will probably be at around this point.
As for the non-royal Nohr units who suffer from the unit imbalancing, Arthur, Effie, and Charlotte were all pretty underwhelming in the chapter they were introduced. You also get Elise in this chapter, who also arrives at a low level, but because she's a healer, it's easy to grind her up throughout most maps. In the following chapter, Nyx arrives at a pretty low level to the point she pretty much did nothing there. In Chapter 17 when you recruit some more Nohr units, Niles arrives at a rather low level for that point in the game, but not as low as Odin, who will most likely be used as pair-up fodder for Leo in that chapter.
The above three paragraphs assumes you will not do any outside grinding as you play through the game. If you do grind between chapters, units like Rinkah, Hana, Subaki, Arthur, Effie, Charlotte, Nyx, Niles, and Odin can be just as good as the rest of your units. I remember grinding up Arthur and Effie following Chapter 14 so that they were caught up with my other units, and both did very well in Chapter 15. Similarly, I grinded up Nyx after clearing Chapter 15, and she did pretty well during Chapter 16 when paired with Hayato.
