Hola Trey!

''Estuve'' es utilizado en pasado junto con el gerundio. It´s used for accions you were doing for a long while:

Ej:

¿Qué estuviste haciendo ayer? Te llamé y no atendiste el teléfono

Estuve trabajando toda la tarde/ Estuve en el trabajo hasta la noche

´´Estaba'' es para preguntar sobre un tiempo específico o para acciones que no terminaste de hacer.

Ej:

¿Donde estabas cuando te llamé? ¿Qué estabas haciendo a las 12:00 pm? (Tiempo específico)

Estaba haciendo ejercicio, pero me cansé. (No finished)   

Estaba lloviendo, pero la lluvia se detuvo.

En cuanto a los lugares,  ''estuve'' se utiliza para lugares que visitaste en el pasado, en los que te quedaste por un tiempo .

Ej:

La semana pasada, estuve en Europa.

Estuve en casa de mi abuela toda la mañana

''Estaba'' se refiere a un lugar en el que estuviste recientemente por un corto tiempo:

Ej: Estaba en mi habitación usando la computadora

     Estaba en el baño

Both are past tense, the difference is that one is imperfect past tense, and the other one is the preterite I assume Romance languages share this particular trait (at least Spanish and French does). Yo "estaba" is imperfect, yo "estuve" is preterite. The imperfect is used when an action in the past is not completed, lasted for a long time, or was repetitive. The preterite is used when the action concluded in the past. Also, there is a particular case in which if you are explaining a past situation and something interrupted said action (also in the past) you use the imperfect for what was interrupted, and the preterite for the action that caused the interruption.  

Example:

Yo estaba (imperfect) en casa cuando Juan me llamó (preterite). (I was  home when Juan called me).

Hoy [yo (subject can be ommited)] estuve (preterite) cocinando. (I was cooking today) Pay attention to the action (cooking), the subject concluded aforementioned action.

El perro me despertó (preterite) con sus ladridos. (The dog woke me up with its barking).

A good example I always use is the Spanish translation of "I loved you".

Yo te amé (preterite meaning I loved you, but I stopped doing so).

Yo te amaba (imperfect meaning I loved you as well, but the action is not finished. So, somehow you still love the person).

I will provide a link that explains a bit the differences. 

http://www.studyspanish.com/lessons/pretimp1.htm.

It takes time and practice to get used to these differences. It took me a month or so to get used to the differences in French (even if I am used to these tenses because of Spanish). 

Hope this helps!

They're both simple past tense forms, the main difference is in the ASPECT of the tense:

"Estaba" is imperfect, meaning actions in progress, continuous, constant/repetitive. "Estaba comiendo" - I was eating. "Estaba en casa" - I was home

"Estuve" is perfect, meaning finished actions, typically one off. "Ayer estuve con tu hermano to-do el dia" - "yesterday I was with your brother all day"

Yes, you can say "Ayer estaba en casa, descansando" and "Ayer estuve en casa, descansando". The former emphasises the progress/duration of the action, and doesn't imply successful completion (maybe you were interrupted later, or the focus of the sentence is something else). The latter clearly establishes that you completed the action successfully. 

If you don't have any context to clearly delimitbwhether the focus is in the result of the action, or in the progress of the action, then you could translate "I was" with either "estaba" or "estuve" (estaba maybe would be more popular because in the absence of context, it's less definitive, whereas with 'estuve' you're definitely conveying information about the result of the action)

Hope that's clear!