Look up body weight exercises (e.g. pushups, dips, etc.) and those which can be done with small easy to carry equipment like resistance bands. Also, running outside or up the stairs in the hotel or swimming in the hotel pool can be used to get cardio exercise. Jump rope is another possibility. That way, you won't have to forego your exercise just because there is no gym, or a gym without the desired equipment (though if you normally do things that does require equipment like heavy free weights, you may have to do something different while traveling).

Walking up the stairs in the hotel or walking to nearby places can give you exercise while getting you to where you are going.